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## Cohomology Rings of the Plactic Monoid via a Grobner--Shirshov basis

Journal of Algebra and its Applications. 2016. Vol. 15. No. 4. Article 1650082.

In this paper, we calculate the cohomology ring and the Hochschild cohomology ring of the plactic monoid algebra via the Anick resolution using a Gröbner–Shirshov basis.

Smirnov E., М. : МЦНМО, 2014

Сколько есть способов разбить натуральное число в сумму нескольких слагаемых, если суммы, отличающиеся только порядком слагаемых, считаются одинаковыми? Оказывается, что простого ответа на этот, казалось бы, элементарный вопрос дать не получается. Зато теория, начинающаяся с этого вопроса, оказывается очень интересной, а ее результаты находят свое применение в самых разных разделах математики и математической физики.
Настоящая брошюра ...

Added: December 2, 2013

Kuznetsov A., Journal fuer die reine und angewandte Mathematik 2015 Vol. 2015 No. 708 P. 213-243

We define the normal Hochschild cohomology of an admissible subcategory of the derived category of coherent sheaves on a smooth projective variety $X$ --- a graded vector space which controls the restriction morphism from the Hochschild cohomology of $X$ to the Hochschild cohomology of the orthogonal complement of this admissible subcategory. When the subcategory is ...

Added: December 22, 2013

Bokut L., Chen Y., Kalorkoti K. et al., World Scientific, 2020

The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac–Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple ...

Added: September 27, 2021

Khoroshkin A., Dotsenko V., Documenta Mathematica 2013 Vol. 18 P. 707-747

The main goal of this paper is to present a way to compute Quillen homology of a shuffle operad with a known Grobner basis. Similar to the strategy taken in a celebrated paper of David Anick, our approach goes in several steps. We define a combinatorial resolution for the ``monomial replacement'' of a shuffle operad, ...

Added: September 29, 2013

Khoroshkin A., Piontkovski D., / Cornell University. Series math "arxiv.org". 2014. No. arXiv:1202.5170.

Given an operad P with a finite Grobner basis of relations, we study the generating functions for the dimensions of its graded components P(n). Under moderate assumptions on the relations we prove that the exponential generating function for the sequence {dim P(n)} is differential algebraic, and in fact algebraic for P is a symmetrization of ...

Added: May 13, 2014

Mironov A., Morozov A., Natanzon S. M., Journal of Knot Theory and Its Ramifications 2014 Vol. 23 No. 6 P. 1-16

The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and arbitrary bipartite graphs. It ...

Added: April 2, 2014

Khoroshkin A., Dotsenko V., Algebra & Number Theory 2013 Vol. 7 No. 3 P. 673-700

This paper has been started as a particular application of the method of resolutions via Grobner bases we suggested here. We introduce a notion of a shuffle algebra. A shuffle algebra is a Z+-graded vector space V=∪∞i=1 such that for any pair (i,j) there exists a collection of operations ∗σ:Vi⊗Vj→Vi+j numbered by (i,j)-shuffle permutations σ∈Si+j ...

Added: September 29, 2013

A.I. Zobnin, Programming and Computer Software 2010 Vol. 36 No. 2 P. 75-82

This survey paper presents general approach to the wellknown F5 algorithm for calculating
Gröbner bases, which was created by Faugère in 2002. ...

Added: October 1, 2014

Basalaev A., Ionov A., Journal of Geometry and Physics 2022 Vol. 174 Article 104450

For a polynomial f=x_1^n+…+x_N^n let Gf be the non–abelian maximal group of symmetries of f. This is a group generated by all g in GL(N,C), rescaling and permuting the variables, so that f(x)=f(g x). For any G subgroup in Gf we compute explicitly Hochschild cohomology of the category of G–equivariant matrix factorizations of f. We ...

Added: September 9, 2022

Kaledin D., Lowen W., Advances in Mathematics 2015 Vol. 272 P. 652-698

We use (non-)additive sheaves to introduce an (absolute) notion of Hochschild cohomology for exact categories as Ext's in a suitable bisheaf category. We compare our approach to various definitions present in the literature. ...

Added: February 9, 2015

Lopatkin V., Journal of Algebra 2019 Vol. 520 P. 59-89

In this paper, we describe the K-module HH1(LK(Γ)) of outer derivations of the Leavitt path algebra LK(Γ) of a row-finite graph Γ with coefficients in an associative commutative ring K with unit. We explicitly describe a set of generators of HH1(LK(Γ)) and relations among them. We also describe a Lie algebra structure of outer derivation algebra of the Toeplitz algebra. We prove that every derivation of a ...

Added: October 29, 2021

Tolmachov K., / Cornell University. Series arXiv:1202.1806 "ArXiv.org". 2012.

In this paper we compute the precise asymptotics of the variance of linear statistic of descents on a growing interval for Plancherel Young diagrams (following Vershik and Kerov, diagrams are considered rotated by π/4). We also give an example of a local configuration with linearly growing variance in a fixed regime and prove the central limit ...

Added: December 8, 2013

Bufetov A. I., Geometric and Functional Analysis 2012 Vol. 22 No. 4 P. 938-975

Vershik and Kerov conjectured in 1985 that dimensions of irreducible representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to the Plancherel family of measures on the space of Young diagrams. The statement of the Vershik-Kerov conjecture can be seen as an analogue of the Shannon-McMillan-Breiman Theorem for the non-stationary ...

Added: October 18, 2012

Van H. D., Lowen W., Advances in Mathematics 2018 Vol. 330 P. 173-228

The aim of this work is to construct a complex which through its higher structure directly controlls deformations of general prestacks, building on the work of Gerstenhaber and Schack for presheaves of algebras. In defining a Gerstenhaber–Schack complex for an arbitrary prestack , we have to introduce a differential with an infinite sequence of components instead of ...

Added: September 13, 2018

Alexandrov D. E., Galkin V. V., Zobnin A.I. et al., Journal of Mathematical Sciences 2009 Vol. 163 No. 5 P. 469-486

Sequential and parallel implementations of the F4 algorithm for computing Gr¨obner bases of
polynomial ideals are discussed. ...

Added: October 1, 2014

Kharitonov V., Khoroshkin A., Annali di Matematica Pura ed Applicata 2022 No. 201 P. 203-241

In this work, we develop the machinery of Grobner bases for coloured operads, which allows us to establish a useful criterion of Koszulness of a coloured operad. Among the examples for which we show the existence of a quadratic Grobner basis, we consider the seminal Lie-Rinehart operad whose algebras include pairs (functions, vector fields). ...

Added: September 8, 2021

Kuznetsov A., / Cornell University. Series math "arxiv.org". 2012. No. 1211.4693.

We define the normal Hochschild cohomology of an admissible subcategory of the derived category of coherent sheaves on a smooth projective variety $X$ --- a graded vector space which controls the restriction morphism from the Hochschild cohomology of $X$ to the Hochschild cohomology of the orthogonal complement of this admissible subcategory. When the subcategory is ...

Added: October 4, 2013

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

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

Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.

We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...

Added: March 9, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019