• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Lascoux Polynomials and Subdivisions of Gelfand–Zetlin Polytopes
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 11, 2026
How to Assess Students Knowledge in the Age of AI
A researcher at HSE University has proposed a flowchart to help lecturers decide how to assess students who use artificial intelligence. It shows where the use of AI should be restricted and where it can be incorporated into the learning process. The article has been published in IT Professional.
September 9, 2026
‘Balkan Hospitality Opens Doors: Studying Dialects on the Verge of Extinction
You cannot study spoken dialects from books. Instead, you need to go to a village, seek out its elders, and earn the trust of local residents before you can record hours of spontaneous stories. This is how Natalia Muravleva, Associate Professor at the Faculty of Humanities, conducts her research. Her internship in Serbia continued her long-standing study of dialects spoken by Macedonian settlers. In this interview, she discusses how diaspora cultural centres help researchers reach informants, why native speakers need to be interviewed only in their own language (otherwise, as she puts it, they may 'break'), and how a single field season helped her finalise her monograph. She also shares warm memories of autumn in Belgrade and of colleagues with whom grammar can be discussed in three languages at once.
September 9, 2026
Scientists Train Neural Network to Generate Process Plans from 3D Models
Researchers at the HSE FCS AI and Digital Science Institute have developed CAD2TechSpec, a framework that converts 3D models of mechanical parts into machining process plans—step-by-step instructions for machine tools. The solution aims to reduce the time required for the design and preparation of technical process documentation in mechanical engineering, aircraft manufacturing, and other high-tech industries. The study findings have been published in PeerJ Computer Science.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Lascoux Polynomials and Subdivisions of Gelfand–Zetlin Polytopes

International Mathematics Research Notices. 2024. Vol. 2024. No. 19. P. 12954–12977.
Presnova E., Smirnov E.

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.

Research target: Mathematics
Language: English
Full text
DOI
Text on another site
Keywords: многогранник Гельфанда-ЦетлинаGelfand-Zetlin polytopeDemazure modulesLascoux polynomialмногочлен Ласкумодуль Демазюра
Publication based on the results of:
Toric geometry and its generalizations (2024)
Similar publications
Характеристические алгебры и интегрируемые системы экспоненциального типа
Смирнов С. В., Миллионщиков Д. В., Уфимский математический журнал 2021 Т. 13 № 2 С. 44–73
В данной работе изучаются характеристические алгебры для систем экспоненциального типа, соответствующих вырожденным матрицам Картана. Эти системы обобщают хорошо известные в теории интегрируемых систем гиперболические уравнения синус-Гордон и Цицейки. Для таких систем, соответствующих матрицам Картана ранга 2, характеристические алгебры описаны явно в терминах образующих и соотношений, и доказано, что они имеют линейный рост. Исследуется связь между ...
Added: September 11, 2026
Darboux formulae for linear hyperbolic equations in the discrete case
Смирнов С. В., Glasgow Mathematical Journal 2026 Vol. 68 No. 2 P. 299–316
In the second half of the 19th century Darboux obtained determinant formulae that provide the general solution for a linear hyperbolic second order PDE with finite Laplace series. These formulae played an important role in his study of the theory of surfaces and, in particular, in the theory of conjugate nets. During the last three ...
Added: September 11, 2026
Integral preserving discretization of 2D Toda lattices
Смирнов С. В., Journal of Physics A: Mathematical and Theoretical 2023 Vol. 56 No. 26 Article 265204
There are different methods of discretizing integrable systems. We consider semi-discrete analog of two-dimensional Toda lattices associated to the Cartan matrices of simple Lie algebras that was proposed by Habibullin in 2011. This discretization is based on the notion of Darboux integrability. Generalized Toda lattices are known to be Darboux integrable in the continuous case ...
Added: September 11, 2026
ВЕРОЯТНОСТНЫЕ МОДЕЛИ РАЗМЕЩЕНИЯ ПО ЯЧЕЙКАМ СЛУЧАЙНОГО ЧИСЛА ЧАСТИЦ
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 132–138
In schemes S for placing r particles in n distinguishable cells, their placement in selected m cells – schemes S∗ is studied, for which the analysis is carried out by a new enumerative method (EM) in extended areas of enumerative combinatorics: finding the number of outcomes and, based on the construction of a model of ...
Added: September 11, 2026
КОМБИНАТОРНЫЙ АНАЛИЗ СХЕМ РАЗМЕЩЕНИЯ ЧАСТИЦ С ЗАДАННЫМ МАКСИМАЛЬНЫМ УРОВНЕМ ЗАПОЛНЕНИЯ ЯЧЕЕК
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 139–147
The class of particle cell arrangements under consideration is characterized by the introduction of an upper limit on the filling levels of the cells, which must be achieved in at least one cell of each outcome of each arrangement. The circuits are distinguished by the paired qualities of their constituent elements (cells and particles) according ...
Added: September 11, 2026
Многокритериальные задачи с упорядоченными по важности группами критериев (II). Решающие правила
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 8 С. 110–123
Для многокритериальных задач принятия решений по аналогии с качественной вероятностью введены понятия полной и частичной качественной важности как бинарных отношений, обладающих постулируемыми свойствами. Предложено новое определение отношения нестрогого предпочтения на множестве вариантов решений, порождаемое качественной важностью. Исследованы его свойства. Указаны аналитические правила, позволяющие попарно сравнивать варианты по предпочтительности. Проведено сравнение новых отношений предпочтения с разработанными ранее для задач, ...
Added: September 9, 2026
Теоретические основы и методы анализа решений в условиях неопределенности при качественных оценках вероятностей и предпочтений
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 7 С. 113–126
Рассматриваются задачи принятия решений, когда предпочтения оцениваются в порядковой шкале, а возможности реализации значений неопределенного фактора описываются качественной вероятностью (полной или только частичной). Вводятся определения отношений предпочтения и безразличий на множестве стратегий. Предлагаются простые решающие правила, позволяющие сравнивать стратегии по предпочтительности, и приводятся иллюстративные примеры. ...
Added: September 9, 2026
Degree-based topological co-indices for QSPR modelling of benzenoid hydrocarbons: a comparative computational study
Chemical Papers 2026
Benzenoid hydrocarbons are structurally regular aromatic compounds, which makes them well suited for quantitative structure–property relationship (QSPR) studies. This study presents a QSPR analysis of nineteen benzenoid hydrocarbon species using degree-based topological co-indices. We developed a Python program to compute eleven degree-based topological co-indices from molecular graphs and evaluated their ability to explain variations in ...
Added: September 8, 2026
On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
On exotic rationally integrable dual billiards I. Complex geometry and type of dynamics.
Glutsyuk A., / Series arXiv "math". 2026.
A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...
Added: September 8, 2026
Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking
Alexandrov A., Glutsyuk A., Journal of Differential Equations 2026 Vol. 465 Article 114178
The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on ...
Added: September 8, 2026
On rationally integrable planar dual and projective billiards
Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...
Added: September 8, 2026
Rational p-adic Hodge theory for d-de Rham-proper stacks
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Lower Bounds on the Measure of the Support of Positive and Negative Parts of Trigonometric Polynomials
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f  is bounded from below by the Motzkin density. We generalize the bound to polynomials in several variables and almost periodic functions. We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Variational representation of weighted divergencies and error exponent function
Kelbert M., Statistics 2026 Vol. 60
We present variational representations for the weighted divergencies and exponential error function, and discuss implications for the statistical inference and entropic optimal transport. ...
Added: September 7, 2026
Конечные последовательности и перестановки, ими порождаемые
Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...
Added: September 7, 2026
Относительные аналитические законы взаимности
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Lascoux Polynomials and Gelfand-Zetlin Patterns
Presnova E., Smirnov E., 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. ...
Added: October 15, 2024
Lascoux polynomials and subdivisions of Gelfand-Zetlin polytopes
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
Beilinson–Drinfeld Schubert varieties and global Demazure modules
Ilya Dumanski, Evgeny Feigin, Michael Finkelberg, Forum of Mathematics, Sigma 2021 Vol. 9 P. 1–25
We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson–Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra. ...
Added: May 25, 2021
PBW Degenerate Schubert Varieties: Cartan Components and Counterexamples
Makhlin I., Algebras and Representation Theory 2020 Vol. 23 No. 6 P. 2315–2330
In recent years PBW degenerations of Demazure modules and Schubert varieties were defined and studied in several papers. Various interesting properties (such as these PBW degenerations embedding naturally into the corresponding degenerate representations and flag varieties) were obtained in type A but only with restrictions on the Weyl group element or the highest weight. We ...
Added: November 11, 2020
Reduced arc schemes for Veronese embeddings and global Demazure modules
Dumanski, I., Feigin E., / Series math "arxiv.org". 2019. No. 1912.07988.
We consider the projective arc schemes of the Veronese embeddings of the flag varieties for simple Lie groups of type ADE. The arc schemes are not reduced and we consider the homogeneous coordinate rings of the corresponding reduced schemes. We show that each graded component of a homogeneous coordinate ring is a cocyclic module of the current algebra and ...
Added: December 18, 2019
Extremal part of the PBW-filtration and nonsymmetric Macdonald polynomials
Cherednik I., Feigin E., Advances in Mathematics 2015 Vol. 282 P. 220–264
Given a reduced irreducible root system, the corresponding nil-DAHA is used to calculate the extremal coefficients of nonsymmetric Macdonald polynomials in the limit t→∞ and for antidominant weights, which is an important ingredient of the new theory of nonsymmetric q-Whittaker function. These coefficients are pure q-powers and their degrees are expected to coincide in the ...
Added: September 3, 2015
Divided difference operators on polytopes
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
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit