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Слайд-многочлены и комплексы подслов
С. 43–44.
We define simplicial complexes for slide polynomials and show that they are always homeomorphic to balls or spheres.
In book
Самара: Инсома-пресс, 2018.
Kiritchenko V., Journal of Combinatorial Theory, Series A 2025 Vol. 213 Article 106022
We construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations give a uniform construction of Knutson–Miller mitosis in the type A and Fujita mitosis in the type C on Kogan faces of Gelfand–Zetlin ...
Added: March 18, 2025
Deviatov R., / Series arXiv "math". 2025.
We sketch the proof of a connection between the canonical (0-)dimension of semisimple split simply connected groups and cohomology of their full flag varieties. Using this connection, we get a new estimate of the canonical (0-)dimension of simply connected split exceptional groups of type E understood as a group. ...
Added: March 12, 2025
Kiritchenko V., Padalko M., , in: Interactions with Lattice Polytopes Magdeburg, Germany, September 2017.: Springer, 2022. P. 233–249.
A Newton–Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent Schubert cycles by linear combinations of faces of the polytope so that the intersection product of cycles corresponds to the set-theoretic intersection of faces (whenever the latter are transverse). We explain the ...
Added: January 31, 2023
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
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
Mathematical Society of Japan, 2016.
This volume contains the proceedings of the 5th MSJ Seasonal Institute on Schubert Calculus, held at Osaka City University, from September 17–27, 2012. It is recommended for all researchers and graduate students who are interested in Schubert calculus and its many connections and applications to related areas of mathematics, such as geometric representation theory, combinatorial ...
Added: October 19, 2020
Smirnov E., Тутубалина А. А., / 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
Kiritchenko V., Padalko M., / Series arXiv "math". 2018.
A Newton-Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent Schubert cycles by linear combinations of faces of the polytope so that the intersection product of cycles corresponds to the set-theoretic intersection of faces (whenever the latter are transverse). We explain the ...
Added: October 15, 2019
Degtiarev Konstantin Y., , in: Proceedings of the 8-th International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control (ICSCCW-2015).: Kaufering: b-Quadrat Verlag, 2015. P. 45–55.
In this paper we propose probability-theoretic approach to compare intervals with rigorous bounds which opens a door to more adequate forms of representation and processing of expert estimates uncertainty ...
Added: February 28, 2016
Valentina Kiritchenko, Mathematical Research Letters 2016 Vol. 23 No. 4 P. 1069–1096
We describe an elementary convex geometric algorithm for realizing Schubert cycles in complete flag varieties by unions of faces of polytopes. For GL_n and Gelfand{Zetlin polytopes, combinatorics of this algorithm coincides with that of the mitosis on pipe dreams introduced by Knutson and Miller. For Sp_4 and a Newton{Okounkov polytope of the symplectic flag variety, ...
Added: February 25, 2016
Kiritchenko V., / Series math "arxiv.org". 2014.
We describe an elementary convex geometric algorithm for realizing Schubert cycles in complete flag varieties by unions of faces of polytopes. For GL_n and Gelfand--Zetlin polytopes, combinatorics of this algorithm coincides with that of the mitosis on pipe dreams introduced by Knutson and Miller. For Sp_4 and a Newton--Okounkov polytope of the symplectic flag variety, ...
Added: September 17, 2014
Valentina Kiritchenko, , in: Oberwolfach ReportsVol. 11. Issue 2.: Zürich: European Mathematical Society Publishing house, 2014. P. 1484–1487.
In [K], a convex-geometric algorithm was introduced for building new analogs of Gelfand–Zetlin polytopes for arbitrary reductive groups. Conjecturally, these polytopes coincide with the Newton–Okounkov polytopes of flag varieties for a geometric valuation. I outline an algorithm (geometric mitosis) for finding collec- tion of faces in these polytopes that represent a given Schubert cycle. For ...
Added: June 23, 2014