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Combinatorial point configurations and polytopes
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The monograph is dedicated to exploring combinatorial point configurations derived from mapping a set of combinatorial configurations into Euclidean space. Various methods for this mapping, along with the typology and properties of the resultant configurations, are presented. In addition, the study revolves around combinatorial polytopes defined as convex hulls of combinatorial point configurations. The primary focus lies in examining multipermutation and partial multipermutation point configurations alongside their associated combinatorial polytopes known as multipermutohedra and partial multipermutohedra. Our theoretical contributions are substantiated through the proof of theorems and supporting auxiliary statements. Examples and illustrations are included to enhance the comprehension of the material.
Anjos, M.F., Lasserre, J.B.: Handbook on Semidefinite, Conic and Polynomial Optimization. Springer, 2012th edn.
Aprile, M., Cevallos, A., Faenza, Y.: On Vertices and Facets of Combinatorial 2-Level Polytopes. In: Combinatorial Optimization. pp. 177–188. Springer, Cham (May 2016). https://doi.org/10.1007/978-3-319-45587-7_16
Balas, E., Ceria, S., Cornu´ejols, G.: A lift-and-project cutting plane algorithm for mixed 0–1 programs. Mathematical Programming 58(1-3), 295–324 (Jan 1993). https://doi.org/10.1007/BF01581273
Balinski, M.L., Hoffman, A.J. (eds.): Polyhedral Combinatorics: Dedicated to the Memory of D.R.Fulkerson. Elsevier Science Ltd, Amsterdam ; New York : New York (1978)
Baumeister, B.: On permutation polytopes. Advances in Mathematics 222(2), 431–452 (Oct 2009), http://resolver.scholarsportal.info/resolve/00018708/v222i0002/431_-opp.xml
Berge, C.: Principles of Combinatorics. Academic Press (Apr 2012)
Bergeron, F., Labelle, G., Leroux, P.: Combinatorial Species and Tree-like Structures.
Cambridge University Press, Cambridge ; New York, NY, USA, 1st edn. (Nov 1997) 219
Bohn, A., Faenza, Y., Fiorini, S., Fisikopoulos, V., Macchia, M., Pashkovich, K.: Enumeration of 2-Level Polytopes. In: Algorithms - ESA 2015, pp. 191–202. Springer, Berlin, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48350-3_17
Bona, M.: Combinatorics of Permutations. Chapman and Hall/CRC, 2nd edn. (Apr 2016)
Brualdi, R.A.: Combinatorial matrix classes. Encyclopedia of Mathematics and its Applications, 108., Cambridge University Press, Cambridge (2006)
Colbourn, C.J.: Handbook of Combinatorial Designs. CRC Press (2010), google-Books-ID: g6LDYlJ36CgC
Deza, A., Fukuda, K., Mizutani, T., Vo, C.: On the face lattice of the metric polytope. In: Akiyama, J., Kano, M. (eds.) Discrete and Computational Geometry. pp. 118–128. Lecture Notes in Computer Science, Springer (2003). https://doi.org/10.1007/978-3-540-44400-8_12
Dixon, J.D., Mortimer, B.: Permutation Groups. Springer, New York, USA, 1996 edn.n(Apr 1996)
Donets, G.O., Koliechkina, L.: Extremal problems on combinatorial configurations. RVV PUET, Poltava, Ukraine (2011), Bibliography http://dspace.puet.edu.ua/handle/123456789/560
Emets’, O.O., Roskladka, O.V., Nedobachii, S.I.: Irreducible System of Constraints for a General Polyhedron of Arrangements. Ukrainian Mathematical Journal 55(1), 1–12 (Jan 2003). https://doi.org/10.1023/A:1025060316418
Fiorini, S., Fisikopoulos, V., Macchia, M.: Two-Level Polytopes with a Prescribed Facet. In: Combinatorial Optimization. pp. 285–296. Springer, Cham (May 2016). https://doi.org/10.1007/978-3-319-45587-7_25
Grande, F., Ru´e, J.: Many 2-Level Polytopes from Matroids. Discrete & Computational Geometry 54(4), 954–979 (Oct 2015). https://doi.org/10.1007/s00454-015-9735-5
Gricik, V.V., Shevchenko, A.I., Kiselyova, O., Yakovlev, S., Stetsyuk, P.: Mathematical methods of optimization and intellectual computer technologies of modeling of complex processes and systems with considering object space forms. Education and Science, Doneck, Ukraine (2012), http://www.ams.org/mathscinet-getitem?mr=894255
Gropp, H.: Configurations between geometry and combinatorics. Discrete Applied Mathematics 138(1), 79–88 (Mar 2004). https://doi.org/10.1016/S0166-218X(03)00271-3
Gruber, P.M.: Convex and Discrete Geometry. Springer, softcover reprint of hardcover 1st ed. 2007 edn.
Grunbaum, B.: Configurations of Points and Lines. American Mathematical Society, Providence, R.I, new edn. (Jun 2009)
Harary, F., Hayes, J.P., Wu, H.J.: A survey of the theory of hypercube graphs. Computers & Mathematics with Applications. An International Journal 15(4), 277–289 (1988)
Henk, M., Richter-Gebert, J., Ziegler, G.M.: Basic properties of convex polytopes. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, pp. 243–270. CRC Press, Inc., Boca Raton, FL, USA (1997), http://dl.acm.org/citation.cfm?id=285869.285884
Hulianytskyi, L.F.: On formalization and classification of combinatorial optimization problems. Optimal Decision Theory 7, 45–49 (2008)
Hulianytskyi, L.F., Mulesa, O.Y.: Applied Methods of Combinatorial Optimization: Tutorial. Publishing and Printing Center "Kyiv University", Kyiv, Ukraine (2016)
Hulianytskyi, L.F., Sirenko, S.I.: Definition and study of combinatorial spaces. Optimal Decision Theory 9, 17–25 (2010)
Hulyanitskii, L.F., Sergienko, I.V.: Metaheuristic downhill simplex method in combinatorial optimization. Cybernetics and Systems Analysis 44(3), 822–829 (May 2008). https://doi.org/10.1007/s10559-008-9011-2
Iemets, O.O., Roskladka, O.V.: Optimization problems on polycombinatorial sets: properties and solutions. RVV PUSKU, Poltava, Ukraine (2006), http://dspace.puet.edu.ua/handle/123456789/377
Kochenberger, G., Hao, J.K., Glover, F., Lewis, M., Lu, Z., Wang, H., Wang, Y.: The unconstrained binary quadratic programming problem: a survey. Journal of Combinatorial Optimization (1), 58–81 (2014). https://doi.org/10.1007/s10878-014-9734-0
Koliechkina, L., Pichugina, O.: A Horizontal Method of Localizing Values of a Linear Function in Permutation-Based Optimization. In: Le Thi, H.A., Le, H.M., Pham Dinh, T. (eds.) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. pp. 355–364. Advances in Intelligent Systems and Computing, Springer International Publishing, Cham (2020). https://doi.org/10.1007/978-3-030-21803-4_36
Korsh, J.F., LaFollette, P.S.: Loopless Array Generation of Multiset Permutations. The Computer Journal 47(5), 612–621 (Jan 2004). https://doi.org/10.1093/comjnl/47.5.612
Korte, B., Vygen, J.: Combinatorial Optimization: Theory and Algorithms. Springer, Heidelberg ; New York, 5th edn. (Jan 2012), 10.1007/978-3-540-71844-4
Kreher, D.L., Stinson, D.R.: Combinatorial Algorithms: Generation, Enumeration, and Search. CRC Press, Boca Raton, Fla, 1st edn. (Dec 1998)
MacMahon, P.A.: Combinatory Analysis. Dover Publications, Mineola, N.Y, dover edn. (Jul 2004)
Martinetti, V.: Sulle configurazioni piane mu3. Annali di Matematica Pura ed Applicata (1867-1897) 15(1), 1–26 (Apr 1887). https://doi.org/10.1007/BF02420228
Onaka, S.: Superspheres: Intermediate Shapes between Spheres and Polyhedra. Symmetry 4(3), 336–343 (Jul 2012). https://doi.org/10.3390/sym4030336
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications, unabridged edn. (1998)
Pardalos, P.M., Du, D.Z., Graham, R.L.: Handbook of Combinatorial Optimization. Springer, 2nd ed. 2013 edn.
Pichugina, O., Yakovlev, S.: Continuous Approaches to the Unconstrained Binary Quadratic Problems. In: B´elair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R.J. (eds.) Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pp. 689–700. Springer International Publishing (2016). https://doi.org/10.1007/978-3-319-30379-6_62
Pichugina, O., Yakovlev, S.: Convex extensions and continuous functional representations in optimization, with their applications. Journal of Coupled Systems and Multiscale Dynamics 4(2), 129–152 (Jun 2016). https://doi.org/10.1166/jcsmd.2016.1103
Pichugina, O., Yakovlev, S.: Continuous Representation Techniques in Combinatorial Optimization. IOSR Journal of Mathematics 13(02), 12–25 (May 2017). https://doi.org/10.9790/5728-1302051225
Pichugina, O., Yakovlev, S.: Optimization on polyhedral-spherical sets: Theory and applications. In: 2017 IEEE 1st Ukraine Conference on Electrical and Computer Engineering, UKRCON 2017 - Proceedings. pp. 1167–1174. Kiev, Ukraine (May 2017). https://doi.org/10.1109/UKRCON.2017.8100436
Pichugina, O., Yakovlev, S.: Quadratic Optimization Models and Convex Extensions on Permutation Matrix Set. In: XIV International Scientific and Technical Conference Computer Science and Information Technologies. Lviv, Ukraine (Sep 2019)
Pichugina, O.S.: The Algorithm of Constructing Convex Extension for Polynomials over Polypermutations and its Applications. Problems of Computer Intellectualization pp. 125–132 (2012), http://www.foibg.com/ibs_isc/ibs-28/ibs-28-p14.pdf
Pichugina, O.S.: Surface and combinatorial cuttings in Euclidean combinatorial optimization problems. Mathematical and computer modelling, The Series: Physics and Mathematics 1(13), 144–160 (Mar 2016), http://mcm-math.kpnu.edu.ua/article/view/70278
Pichugina, O.S.: Functional-analytic representations of Euclidean combinatorial configuration sets in optimization. Radioelectronics & Informatics Journal (1), 30–39 (2018), http://dspace.nbuv.gov.ua/handle/123456789/132017
Pichugina, O.S.: Mathematical modeling of combinatorial configurations and application in optimization. Mathematical machines and systems (1), 123–137 (2018), http://dspace.nbuv.gov.ua/handle/123456789/132017
Pichugina, O.S., Yakovlev, S.V.: Continuous Representations and Functional Extensions in Combinatorial Optimization. Cybernetics and Systems Analysis 52(6), 921–930 (Nov 2016). https://doi.org/10.1007/s10559-016-9894-2
Pichugina, O.S., Yakovlev, S.V.: Convex extensions for the quadratic problems over permutation matrices. Computational Mathematics (1), 143–154 (2016)
Pichugina, O.S., Yakovlev, S.V.: Functional and analytic representations of the general permutation. EasternEuropean Journal of Enterprise Technologie 79(1(4)), 27–38 (2016). https://doi.org/10.15587/1729-4061.2016.58550
Pichugina, O.S., Yakovlev, S.V.: The penalty method for solving optimization problems over polyhedral-spherical combinatorial sets. Radioelectronics & Informatics Journal (1), 18–26 (2016)
Pichugina, O.S., Yakovlev, S.V.: Global optimization on permutohedron in combinatorial problems on vertex-set sets. Mathematical and computer modelling, The Series: Physics and Mathematics 1(15), 152–158 (2017), http://mcm-math.kpnu.edu.ua/article/view/111576
Pichugina, O.S., Yakovlev, S.V.: Continuous functional representations in discrete optimization: a monograph. Gold Mile, Kharkiv, Ukraine (2018)
Pichugina, O.: New Bounds in Linear Combinatorial Optimization. In: Proceedings of the 9th International Conference "Information Control Systems & Technologies". pp. 137–149. CEUR Vol-2711 urn:nbn:de:0074-2711-3, Odessa, Ukraine (Sep 2020)
Pichugina, O., Kartashov, O.: Signed Permutation Polytope Packing in VLSI Design. In: 2019 IEEE 15th International Conference on the Experience of Designing and Application of CAD Systems (CADSM). pp. 4/50–4/55 (Feb 2019). https://doi.org/10.1109/CADSM.2019.8779353
Pichugina, O., Koliechkina, L.: Linear constrained combinatorial optimization on welldescribed sets. IOP Conference Series: Materials Science and Engineering 1099(1), 012064.1–17 (Mar 2021). https://doi.org/10.1088/1757-899X/1099/1/012064
Pichugina, O., Muravyova, N.: A spherical cutting-plane method with applications in multimedia flow management. In: Proceedings of the 1st International Workshop on Digital Content & Smart Multimedia (DCSMart 2019). vol. 2533, pp. 82–93. CEUR (2019), https://ceur-ws.org/Vol-2533/paper8.pdf
Pichugina, O., Muravyova, N.: The Polyhedral-Surface Cutting-Plane Method for Linear Combinatorial Optimization. In: Proceedings of the 9th International Conference "Information Control Systems & Technologies". pp. 455–467. CEUR Vol-2711 urn:nbn:de:0074-2711-3, Odessa, Ukraine (Sep 2020)
Pichugina, O., Yakovlev, S.: Euclidean Combinatorial Configurations: Continuous Representations and Convex Extensions. In: Lytvynenko, V., Babichev, S., Wójcik, W., Vynokurova, O., Vyshemyrskaya, S., Radetskaya, S. (eds.) Lecture Notes in Computational Intelligence and Decision Making. pp. 65–80. Advances in Intelligent Systems and Computing, Springer, Cham, Zalizniy Port, Ukraine (Jul 2019). https://doi.org/10.1007/978-3-030-26474-1_5, 21-25 May
Pichugina, O., Yakovlev, S.: Euclidean Combinatorial Configurations: Typology and Applications. In: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON). pp. 1065–1070 (Jul 2019). https://doi.org/10.1109/UKRCON.2019.8879912
Pichugina, O., Yakovlev, S.: Quadratic Optimization Models and Convex Extensions on Permutation Matrix Set. In: Shakhovska, N., Medykovskyy, M.O. (eds.) Advances in Intelligent Systems and Computing IV. pp. 231–246. Advances in Intelligent Systems and Computing, Springer International Publishing (Nov 2019). https://doi.org/10.1007/978-3-030-33695-0_17, 11-13 September 2019
Pichugina, O.: Polyhedral-spherical configurations: pecularities and applications. Mathematical and computer modelling, The Series: Physics and Mathematics (17), 90–107 (2018), http://mcm-math.kpnu.edu.ua/article/view/140087
Pisanski, T., Servatius, B.: Configurations from a Graphical Viewpoint. Birkh¨auser Advanced Texts Basler Lehrb¨ucher, Birkh¨auser Basel, 1st edn. (2013), http://gen.lib.rus.ec/book/index.php?md5=7a51663351a4844553de6b68c1e77f95
Postnikov, A.: Permutohedra, Associahedra, and Beyond. IMRN: International Mathematics Research Notices 2009(6), 1026–1106 (Mar 2009). https://doi.org/10.1093/imrn/rnn153
Pulleyblank, W.R.: Edmonds, matching and the birth of polyhedral combinatorics. Documenta Mathematica pp. 181–197 (2012)
Rispoli, F.J.: The Graph of the Hypersimplex. arXiv:0811.2981 [math] (Nov 2008), http://arxiv.org/abs/0811.2981, arXiv: 0811.2981
Ryser, H.J.: Combinatorial Configurations. SIAM Journal on Applied Mathematics 17(3), 593–602 (1969). https://doi.org/10.2307/2099147
Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer Science & Business Media (Dec 2002), google-Books-ID: mqGeSQ6dJycC
Schroter, H.: Ueber lineare Constructionen zur Herstellung der Configurationen $n_3$. Gottinger Nachrich pp. 237–253 (1888)
Semenova, N.V., Kolechkina, L.M.: Vector problems of discrete optimization on combinatorial sets: methods of research and solution. Naukova Dumka, Kyiv, Ukraine (2009)
Stoyan, Y.G., Grebennik, I.: Description of classes of combinatorial configurations based on mappings. Dopovidi Natsionalnoi Akademii Nauk
Sergienko, I.V., Hulianytskyi, L.F., Sirenko, S.I.: Classification of applied methods of combinatorial optimization. Cybernetics and Systems Analysis 45(5), 732 (Sep 2009). https://doi.org/10.1007/s10559-009-9134-0
Sergienko, I.V., Shylo, V.P.: Problems of discrete optimization: Challenges and main approaches to solve them. Cybernetics and Systems Analysis 42(4), 465–482 (Jul 2006). https://doi.org/10.1007/s10559-006-0086-3
Sergienko, I.V.: Methods of optimization and systems analysis for problems of transcomputational complexity., Springer optimization and its applications, vol. 72. New York, NY : Springer (2012)
Stoyan, Y.G.: Some properties of special combinatorial sets (1980)
Stoyan, Y.G.: On a mapping of combinatorial sets into the Euclidean space (1992)
Stoyan, Y.G., Yakovlev, S.V.: Mathematical models and optimization methods in Geometric Design. Naukova Dumka, Kiev (1986)
Stoyan, Y.G., Yakovlev, S.V.: Mathematical models and optimization methods in Geometric Design (complemented ed.). Naukova Dumka, Kiev, Ukraine, 2nd edn. (2020)
Stoyan, Y.G., Yakovlev, S.V.: Theory and Methods of Euclidian Combinatorial Optimization: Current Status and Prospects. Cybernetics and Systems Analysis 56(3), 366–379 (May 2020). https://doi.org/10.1007/s10559-020-00253-6
Stoyan, Y.G., Yemets’, O.: Theory and methods of Euclidean combinatorial optimization. ISSE, Kiev, Ukraine (1993)
Stoyan, Y.G., Grebennik, I.: Compositional images of combinatorial sets andsome of their properties. Mechnical Engineering Problems 8(3), 56–62 (2005), http://scholar.google.com/scholar?cluster=6247466018141153953&hl
Stoyan, Y.G., Grebennik, I.: Description of classes of combinatorial configurations based on mappings. Dopovidi Natsionalnoi Akademii Nauk Ukrainy. Matematika. Prirodoznavstvo. Tekhnichni Nauki (10), 28–31 (2008), http://dspace.nbuv.gov.ua/xmlui/handle/123456789/6089
Stoyan, Y.G., Grebennik, I.: Combinatorial types for enumerating combinatorial configurations with special properties. Dopovidi Natsionalnoi Akademii Nauk Ukrainy. Matematika. Prirodoznavstvo. Tekhnichni Nauki (7), 28–32 (2010), http://www.ams.org/mathscinet-getitem?mr=3112750
Stoyan, Y.G., Yakovlev, S.V.: Construction of convex and concave functions on the permutation polyhedron. Dokl. Acad. Sci. USSR A (5), 68–70 (1988), http://www.ams.org/mathscinet-getitem?mr=951554
Stoyan, Y.G., Yakovlev, S.V.: Properties of convex functions on the permutohedron. Doclady of Academy of Sciences of the Ukrainian SSR. Ser. A 88(3), 69–72 (1988)
Stoyan, Y.G., Yakovlev, S.V., Grebennik, I.V.: Extremal problems on the set of arrangements / national academy of sciences of ukraine, institute of mechnical engineering problems, no. 347)
Stoyan, Y.G., Yakovlev, S.V., Parshin, O.V.: Quadratic optimization on combinatorial sets in Rn. Cybernetics and Systems Analysis 27(4), 561–567 (Jul 1991). https://doi.org/10.1007/BF01130367
Stoyan, Y.G., Yakovlev, S.V., Pichugina, O.S.: The Euclidean combinatorial configurations: a monograph. Constanta, Kharkiv, Ukraine (2017)
Toth, C.D., O’Rourke, J., Goodman, J.E.: Handbook of Discrete and Computational Geometry. Chapman and Hall/CRC, 3rd edn.
Yakovlev, S., Pichugina, O., Yarovaya, O.: On Optimization Problems on the Polyhedral-Spherical Configurations with their Properties. In: 2018 IEEE First International Conference on System Analysis Intelligent Computing (SAIC). pp. 94–100. Kyiv, Ukraine (Oct 2018). https://doi.org/10.1109/SAIC.2018.8516801
Yakovlev, S.V.: Bounds on the minimum of convex functions on Euclidean combinatorial sets. Cybernetics 25(3), 385–391 (May 1989). https://doi.org/10.1007/BF01069996
Yakovlev, S.V.: The theory of convex continuations of functions on vertices of convex polyhedra. Computational Mathematics and Mathematical Physics 34(7), 1112–1119 (1994), http://www.ams.org/mathscinet-getitem?mr=1293961
Yakovlev, S.V.: The convex extension theory in combinatorial optimization problems. Dopovidi Natsionalnoi Akademii Nauk Ukrainy.
Matematika. Prirodoznavstvo. Tekhnichni Nauki (8), 20–26 (2017). https://doi.org/http://dx.doi.org/10.15407/dopovidi2016.02.031
Yakovlev, S.V.: On the combinatorial structure of problems of geometric design. Dopovidi Natsionalnoi Akademii Nauk Ukrainy. Matematika. Prirodoznavstvo. Tekhnichni Nauki (9), 26–32 (2017). https://doi.org/http://dx.doi.org/10.15407/dopovidi2016.02.031
Yakovlev, S.V., Gil, N., Komyak, V., Aristova, I.: Elements of the geometric design theory: Monograph. Naukova Dumka, Kiev, Ukraine (1995)
Yakovlev, S.V., Grebennik, I.V.: Some classes of optimization problems on a set of arrangements and their properties. Izvestiya Vysshikh Uchebnykh Zavedeniuı. Matematika (11), 74–86 (1991), http://www.ams.org/mathscinet-getitem?mr=1179093
Yakovlev, S.V., Grebennik, I.V.: Localization of solutions of some problems of nonlinear integer optimization. Cybernetics and Systems Analysis 29(5), 727–734 (Sep 1993). https://doi.org/10.1007/BF01125802
Yakovlev, S.V., Pichugina, O.S.: Properties of Combinatorial Optimization Problems Over Polyhedral-Spherical Sets. Cybernetics and Systems Analysis 54(1), 99–109 (Feb 2018). https://doi.org/10.1007/s10559-018-0011-6
Yakovlev, S.: Convex Extensions in Combinatorial Optimization and Their Applications. In: Optimization Methods and Applications, pp. 567–584. Springer Optimization and Its Applications, Springer, Cham (2017),https://link.springer.com/chapter/10.1007/978-3-319-68640-0_27,10.1007/978-3-319-68640-0_27
Yakovlev, S.V., Pichugina, O.S., Yarovaya, O.V.: Polyhedral-Spherical Configurations in Discrete Optimization Problems. Journal of Automation and Information Sciences 51(1), 26–40 (2019). https://doi.org/10.1615/JAutomatInfScien.v51.i1.30
Yakovlev, S., Kartashov, O., Pichugina, O.: Optimization on Combinatorial Configurations Using Genetic Algorithms. In: Proceedings of the Second International Workshop on Computer Modeling and Intelligent Systems (CMIS-2019). pp. 28–40. CEUR Vol-2353 urn:nbn:de:0074-2353-0, Zaporizhzhia, Ukraine (Apr 2019), http://ceur-ws.org/Vol-2353/paper3.pdf
Yakovlev, S., Kartashov, O., Pichugina, O., Korobchynskyi, K.: Genetic Algorithms for Solving Combinatorial Mass Balancing Problem. In: 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON). pp. 1061–1064 (Jul 2019). https://doi.org/10.1109/UKRCON.2019.8879938
Yakovlev, S., Kartashov, O., Yarovaya, O.: On Class of Genetic Algorithms in Optimization Problems on Combinatorial Configurations. In: 2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT). vol. 1, pp. 374–377 (Sep 2018). https://doi.org/10.1109/STC-CSIT.2018.8526746
Yakovlev, S., Pichugina, O.: On Constrained Optimization of Polynomials on Permutation Set. In: CMIS (2019)
Yakovlev, S.: On a combinatorial structure of the problems of optimal packing of geometric objects. Dopovidi Natsionalnoi Akademii Nauk Ukrainy. Matematika. Prirodoznavstvo. Tekhnichni Nauki (9), 26–32 (2017). https://doi.org/10.15407/dopovidi2017.09.026
Yakovlev, S.: The theory of convex extensions in combinatorial optimization problems (8), 20–26 (2017). https://doi.org/10.15407/dopovidi2017.08.020
Yemelichev, V.A., Koval¨ev, M.M., Kravtsov, M.K.: Polytopes, graphs and optimisation. Cambridge University Press, Cambridge (1984), http://www.ams.org/mathscinet-getitem?mr=744197, translated from the Russian by G. H. Lawden 10.1112/blms/17.3.281
Yemets, O.O., Barbolina, T.M.: Combinatorial optimization on partial permutations. Naukova Dumka, Kyiv, Ukraine (2008), http://dspace.puet.edu.ua/handle/123456789/473
Yemets, O.O., Koliechkina, L., Nedobachii, S.I.: Study of search domains of Euclidean combinatorial optimization problems on permutation sets. ChPKP Legat, Poltava, Ukraine (1999), http://dspace.puet.edu.ua/handle/123456789/488
Yemets, O.O., Nedobachi˘ı, S.I.: The general permutohedron: an irreducible system of linear constraints and all facets’ equations. Naukovi visti NTUU - KPI (1), 100–106 (1998)
Zgurovsky, M.Z., Pavlov, A.: Hard combinatorial optimization problems in planning and decision making. Naukova Dumka, Kyiv, Ukraine (2016)
Ziegler, G.M.: Lectures on 0/1-Polytopes. In: Kalai, G., Ziegler, G.M. (eds.) Polytopes — Combinatorics and Computation, pp. 1–41. No. 29 in DMV Seminar, Birkh¨auser Basel (2000). https://doi.org/10.1007/978-3-0348-8438-9_1
Ziegler, G.M.: Lectures on Polytopes. Springer, 7th edn. (2011)
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