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Lascoux Polynomials and Gelfand-Zetlin Patterns
Seminaire Lotharingien de Combinatoire. 2024. Vol. 91B. Article 63.
We give a new combinatorial description for Lascoux polynomials and for symmetric Grothendieck polynomials in terms of cellular decompositions of Gelfand– Zetlin polytopes. This generalizes a similar result on key polynomials by Kiritchenko, Smirnov, and Timorin.
Publication based on the results of:
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2026 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Шестопёров А. И., Фомина Е. В., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., International Frequency Sensor Association (IFSA) Publishing, 19-21 February 2025 Granada, Spain 2025 P. 172–176
The paper presents models for an innovative fully robotic warehouse for storing boxed goods. A discrete multiagent simulation of the movement of shuttles in a warehouse for a given sequence of pallet shipments has been implemented. Different strategies for placement of boxes in various areas of a warehouse are evaluated, as well as optimal routing ...
Added: June 26, 2026
Fedorov Timofey, Moscow Mathematical Journal 2026 Vol. 26 No. 1 P. 73–85
We obtain a complete list of smooth projective threefolds over C for which the dimension of the space of vanishing cycles (in H2(Y,Q) of the smooth hyperplane section Y) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c2(E)=3. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,
включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Gadzhimirzaev S., Хельвас А. В., Computer Research and Modeling 2026 Vol. 18 No. 2 P. 423–438
This article presents a model of a fully automated warehouse with deep storage racks designed
for boxed goods storage. The study focuses on optimizing warehouse operations through discrete
multiagent simulation of shuttle movements for pallet loading and unloading tasks. The authors
investigate various product placement strategies, including the Nearest Channel Positioning Algorithm
(NCPA), Most Empty ChannelGroup Placement (MECGP), and ...
Added: June 24, 2026
Gaianov N., Parusnikova A., Уфимский математический журнал 2026 Т. 18 № 2 С. 14–22
We consider an algebraic 𝑞–difference equation. We propose a sufficient condition for the existence of a formal power–logarithmic expansion in the vicinity of zero of the solution to such an equation. We apply this sufficient condition to construct the formal expansion of a solution to a certain 𝑞–difference analogue of the fifth Painlevé equation for
particular ...
Added: June 24, 2026
Presnova E., Smirnov E., International Mathematics Research Notices 2024 Vol. 2024 No. 19 P. 12954–12977
We give a new combinatorial description for Grassmannian Grothendieck polynomials in terms of subdivisions of Gelfand–Zetlin polytopes. Moreover, these subdivisions also provide a description of Lascoux polynomials. This generalizes a similar result on key polynomials by Kiritchenko, Smirnov, and Timorin. ...
Added: September 7, 2024
Presnova E., Smirnov E., / Series math "arxiv.org". 2023. No. 2312.01417.
We give a new combinatorial description for stable Grothendieck polynomials in terms of subdivisions of Gelfand-Zetlin polytopes. Moreover, these subdivisions also provide a description of Lascoux polynomials. This generalizes a similar result on key polynomials by Kiritchenko, Smirnov, and Timorin. ...
Added: February 12, 2024
Valentina Kiritchenko, / Series math "arxiv.org". 2013. No. 1307.7234.
We define convex-geometric counterparts of divided difference (or Demazure) operators from the Schubert calculus and representation theory. These operators are used to construct inductively polytopes that capture Demazure characters of representations of reductive groups. In particular, Gelfand-Zetlin polytopes and twisted cubes of Grossberg-Karshon are obtained in a uniform way. This preprint contains the proofs of ...
Added: October 6, 2013
Kiritchenko Valentina, Timorin Vladlen, Gusev P., Journal of Combinatorial Theory, Series A 2013 Vol. 120 P. 960–969
We discuss the problem of counting vertices in Gelfand--Zetlin polytopes. Namely, we deduce a partial differential equation with constant coefficients on the exponential generating function for these numbers. For some particular classes of Gelfand-Zetlin polytopes, the number of vertices can be given by explicit formulas. ...
Added: February 18, 2013
Kiritchenko V., Smirnov E., Timorin V., Russian Mathematical Surveys 2012 Vol. 67 No. 4 P. 685–719
A new approach is described to the Schubert calculus on complete flag varieties, using the volume polynomial associated with Gelfand- Zetlin polytopes. This approach makes it possible to compute the intersection products of Schubert cycles by intersecting faces of a polytope. Bibliography: 23 titles. ...
Added: February 4, 2013
Kiritchenko V., International Mathematics Research Notices 2010 No. 13 P. 2512–2531
I construct a correspondence between the Schubert cycles on the variety of complete flags in ℂn and some faces of the Gelfand–Zetlin polytope associated with the irreducible representation of SLn(ℂ) with a strictly dominant highest weight. The construction is motivated by the geometric presentation of Schubert cells using Demazure modules due to Bernstein–Gelfand–Gelfand [3]. The ...
Added: November 17, 2012
Kiritchenko V., Smirnov E., Timorin V., Успехи математических наук 2012 Т. 67 № 4 С. 89–128
We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope. ...
Added: September 19, 2012