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Intransitively winning chess players’ positions
Doklady Mathematics. 2024. Vol. 110. No. Suppl 2. P. S391–S398.
Chess players' positions in intransitive (rock-paper-scissors) relations are considered. Intransitivity of chess players' positions means that: position A of White is preferable (it should be chosen if choice is possible) to position B of Black, if A and B are on a chessboard; position B of Black is preferable to position C of White, if B and C are on the chessboard; position C of White is preferable to position D of Black, if C and D are on the chessboard; but position D of Black is preferable to position A of White, if A and D are on the chessboard. Intransitivity of winningness of chess players' positions is considered to be a consequence of complexity of the chess environment--in contrast with simpler games with transitive positions only. The space of relations between winningness of chess players' positions is non-Euclidean. The Zermelo-von Neumann theorem is complemented by statements about possibility vs. impossibility of building pure winning strategies based on the assumption of transitivity of players' positions. Questions about the possibility of intransitive players' positions in other positional games are raised.
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Avdoshin S.M., Patrushev K. A., Proceedings of the Institute for System Programming of the RAS 2026 No. 4 часть 2 P. 245–256
The cardinality-constrained Markowitz problem is NP-hard and traditionally solved with commercial MIQP solvers. Following the 2022 export restrictions that rendered both commercial MIQP software and cloud quantum platforms (IBM Quantum, D-Wave Leap) inaccessible from the Russian Federation, practitioners require open-source alternatives. This paper systematically compares three solver families for the discrete mean-variance problem: two open-source ...
Added: August 27, 2026
Zaikin A., Vlasenko D., Zakharov D. et al., Diagnostics 2026 Vol. 16 No. 17 P. 1–15
Background/Objectives: Synolitic graphs (SGs) were developed for task-based fMRI, where
edge weights encode the discriminative power of pairwise regional features; whether similar
information can be recovered from resting-state data was untested. We benchmarked
SGs for autism spectrum disorder (ASD) classification using the multisite ABIDE-I dataset
(871 subjects: 403 subjects with ASD, 468 typical controls; 17 sites; CC200 atlas). Methods:
Using ...
Added: August 27, 2026
Melnikov I., Pelinovsky E., Nonlinear Dynamics 2026 No. 114 Article 934
Pyramidal solitons (solitons with more than two inflection points) of the generalized Korteweg–de Vries (KdV) equation are investigated. Necessary and sufficient conditions for the existence of such structures are presented. Within the framework of the generalized Gardner equation — the simplest model that admits pyramidal solitons as solutions — it is shown that these solutions ...
Added: August 27, 2026
Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2025.
Сборник содержит материалы, представленные на XXIV Международной конференции «Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: современные проблемы, приложения и проблемы истории», посвящённой 110-летию со дня рождения академика Юрия Владимировича Линника и 110-летию со дня рождения профессора Андрея Борисовича Шидловского и 80-летию со дня рождения профессора Геннадия Ивановича Архипова. Материалы конференции будут полезны научным работникам, ...
Added: August 27, 2026
Nesterenko A., Чирский В. Г., Матвеев В. Ю., Чебышевский сборник 2026 Т. 27 № 2 С. 118–127
The article presents the results of a practical study of the statistical properties of some sequences that are values of functions of a special type. ...
Added: August 26, 2026
Eduard Sopin, Nazarin A., Begishev V. et al., IEEE Transactions on Vehicular Technology 2026 Vol. 75 No. 6 P. 10995–11007
Aimed at rate-greedy applications having extreme requirements for the data rate at the air interface, 5G New Radio (NR) systems may experience problems when the number of user equipment (UE) in the coverage of the cell increases due to limited capacity of the physical downlink control channel (PDCCH).The aim of this study is to explore ...
Added: August 26, 2026
Orekhov B., / Series Computer Science "arxiv.org". 2024.
In this paper, I apply linguistic methods of analysis to non-linguistic data, chess plays, metaphorically equating one with the other and seeking analogies. Chess game notations are also a kind of text, and one can consider the records of moves or positions of pieces as words and statements in a certain language. In this article ...
Added: August 8, 2024
Adhikari A., Anatolyev S., Dagaev D., IEEE TRANSACTIONS ON GAMES 2024 Vol. 16 No. 2 P. 483–488
We investigate how the mistakes of professional chess players affect the quality of their further moves in the same game. Using a database of games played by top chess players, Stockfish chess engine evaluations, and an ordered probit regression analysis, we found clear evidence that most mistakes provoke tilt, which leads to less accurate future play, ...
Added: May 8, 2023
Poddiakov A., Lebedev A., European Journal of Mathematics 2023 Vol. 9 Article 27
Various objects and systems in intransitive relations of superiority (“rock-paper-scissors” relations) are described (intransitive sets of sticks, dice, chess positions, machines, biological species etc.). The concept of meta-intransitivity of superiority is introduced. Meta-intransitivity is a property of systems, which are in intransitive relationships between one another, and, at the same time, each of them contains ...
Added: April 12, 2023
Poddiakov A., , in: Proceedings of the PME and Yandex Russian conference: Technology and Psychology for Mathematics Education.: M.: SU HSE Publishing House, 2019. P. 178–185.
Added: January 3, 2020
Poddiakov A., / Series arXiv "math". 2018. No. 1809.03869.
The intransitive cycle of superiority is characterized by such binary relations between A, B, and C that A is superior to B, B is superior to C, and C is superior to A (i.e., A>B>C>A—in contrast with transitive relations A>B>C). The first part of the article presents a brief review of studies of intransitive cycles ...
Added: September 12, 2018
Poddiakov A., В кн.: Психология когнитивных процессов.: Смоленск: СмолГУ, 2017. С. 52–57.
Nontransitivity of winningness of chess arrangements (i.e., their relations like in the rock-paper-scissors game) is recently found property of chess environment. The concept of interactivity of a game, i.e., extent of its parties’ interaction (interpenetration) is introduced. Games of different interactivity are analyzed, and nontransitivity is considered as a consequence of high interactivity. Consequences of ...
Added: June 19, 2017
Poddiakov A., Психолого-экономические исследования 2016 Т. 3 (9) № 4 С. 43–50
Knowledge from different areas (from mathematics to biology and social and economic psychology) is integrated to show that intransitive relations of superiority (like in Rock-Paper-Scissors game) are a wide-spread law in many complex systems. Its ignoring with “blind” following the principle of transitivity (if A>B and B>C then A>С) increases probability of some kinds of ...
Added: January 23, 2017
Gurvich V., Oudalov V., Discrete Applied Mathematics 2014 Vol. 167 P. 131–143
We study existence of Nash equilibria (NE) in pure stationary strategies in n-person positional games with no moves of chance, with perfect information, and with the mean or total effective cost function.
We construct a NE-free three-person game with positive local costs, thus disproving the conjecture suggested in Boros and Gurvich (2003). Still, the following four problems ...
Added: October 22, 2016
Shitov Y., American Mathematical Monthly 2016 Vol. 123 No. 1 P. 71–77
We present an infinite sequence of pairs (An, Bn) of chess positions on an n × n board such that (1) there is a legal sequence of chess moves leading from An to Bn and (2) any legal sequence leading from An to Bn contains at least exp(n + o(n)) moves. ...
Added: February 23, 2016
Shitov Y., / Series math "arxiv.org". 2014. No. 1409.1530.
We give an example of two n-by-n chess positions, A and B, such that (1) there is a sequence of legal chess moves leading from A to B; (2) the length of this sequence cannot be less than exp(cn). ...
Added: October 30, 2014