?
Pipe dreams for Schubert polynomials of the classical groups
Cornell University
,
2020.
No. 2009.14120.
Smirnov E., Тутубалина А. А.
Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety of a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for the Weyl groups of the classical types.
Smirnov E., Тутубалина А. А., / Cornell University. Series math "arxiv.org". 2020. No. 2006.16995.
Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gröbner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the corresponding Schubert polynomial. In 2017 S.Assaf and D.Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and ...
Added: July 6, 2020
Smirnov E., Тутубалина А. А., Успехи математических наук 2020 Т. 75 № 6(456) С. 177-178
В работе рассматривается подразбиение комплексов подслов, определенных Кнутсоном и Миллером, на слайд-комплексы; показано, что эти комплексы являются шеллинговыми и гомеоморфны шару или сфере. ...
Added: October 28, 2020
Vladimir L. Popov, Zarhin Y., Indiana University Mathematics Journal 2021 Vol. 70 No. 1 P. 285-300
We classify the types of root systems R in the rings of integers of number fields K such that the Weyl group W(R) lies in the group L(K) generated by Aut(K) and multiplications by the elements of K*. We also classify the Weyl groups of root systems of rank n which are isomorphic to a ...
Added: February 27, 2021
Zhgoon V., Кноп Ф., Доклады Российской академии наук. Математика, информатика, процессы управления 2020 Т. 490 № 1 С. 29-34
We construct the action of the restricted Weyl group on the set of principle families
of orbits of a minimal parabolic subgroup over algebraically non-closed eld. Also
we relate this action with the action on polarized cotangent bundle. These results
generalize corresponding results of [1] on the action of the Weyl group on the families
of Borel orbits of ...
Added: October 21, 2019
V. L. Popov, Zarhin Y. G., Doklady Mathematics 2018 Vol. 98 No. 3 P. 600-602
We classify the types of root systems R in the rings of integers of number fields K such that the Weyl
group W(R) lies in the group generated by Aut(K) and multiplications by the elements of K*. ...
Added: December 26, 2018
Smirnov E., Тутубалина А. А., Математический сборник 2021 Т. 212 № 10 С. 131-151
Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gröbner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the corresponding Schubert polynomial. In 2017 S.Assaf and D.Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and ...
Added: September 29, 2021
Merzon G., Smirnov E., / Cornell University. Series math "arxiv.org". 2014. No. 1410.6857.
We prove new determinantal identities for a family of flagged Schur polynomials. As a corollary of these identities we obtain determinantal expressions of Schubert polynomials for certain vexillary permutations. ...
Added: October 23, 2014
Tyurin D., Journal of Combinatorial Theory, Series A 2017 Vol. 154 P. 32-48
The goal of the present paper is to extend the mitosis algorithm, originally developed by Ezra Miller and Allen Knutson for the case of Schubert polynomials, to the case of Grothendieck polynomials. In addition we will also use this algorithm to construct a short combinatorial proof of Fomin–Kirillov's formula for the coefficients of Grothendieck polynomials. ...
Added: September 23, 2017
Smirnov E., Merzon G., European Journal of Mathematics 2016 Vol. 2 No. 1 P. 227-245
We prove new determinantal identities for a family of flagged Schur polynomials. As a corollary of these identities we obtain determinantal expressions of Schubert polynomials for certain vexillary permutations. ...
Added: October 2, 2015
Vassiliev V., М. : МЦНМО, 2020
Рассматривается восходящая к Архимеду и Ньютону задача о зависимости объема, отсекаемого плоскостью от ограниченного тела, от этой плоскости. В частности, мы докажем гипотезу В.И.Арнольда о том, что для тела с гладкой границей в четномерном пространстве этот объем не может алгебраически зависеть от коэффициентов уравнения плоскости, и приведем геометрические препятствия к такой алгебраичности в нечетномерном случае. В ...
Added: November 18, 2020
Evgeny Smirnov, Anna Tutubalina, European Journal of Combinatorics 2023 Vol. 107 Article 103613
Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety over a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for Weyl groups ...
Added: September 14, 2022
Le Floch B., Smilga I., Comptes Rendus Mathematique 2018 Vol. 356 No. 8 P. 852-858
For any simple complex Lie group, we classify irreducible finite-dimensional representations rho for which the longest element w_0 of the Weyl group acts non-trivially on the zero-weight space. Among irreducible representations that have zero among their weights, w_0 acts by Id or -Id if and only if the highest weight of rho is a multiple of a fundamental weight, ...
Added: September 26, 2018
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
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Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
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В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
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