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pro vyhledávání: '"Pawlowski, Brendan"'
Autor:
Marberg, Eric, Pawlowski, Brendan
This semi-expository article presents an inductive method of computing initial ideals and Gr\"obner bases for families of ideals in a polynomial ring. This method starts from a given set of pairs $(I,J)$ where $I$ is any ideal and $J$ is a monomial i
Externí odkaz:
http://arxiv.org/abs/2412.17320
Autor:
Pawlowski, Brendan
Publikováno v:
In Linear Algebra and Its Applications 1 December 2024 702:98-111
Autor:
Marberg, Eric, Pawlowski, Brendan
Publikováno v:
Adv. Math. 405 (2022), 108488
Matrix Schubert varieties are the closures of the orbits of $B\times B$ acting on all $n\times n$ matrices, where $B$ is the group of invertible lower triangular matrices. Extending work of Fulton, Knutson and Miller identified a Gr\"obner basis for
Externí odkaz:
http://arxiv.org/abs/2010.00653
Autor:
Pawlowski, Brendan
Huang, McKinnon, and Satriano conjectured that if $v \in \mathbb{R}^n$ has distinct coordinates and $n \geq 3$, then a hyperplane through the origin other than $\sum_i x_i = 0$ contains at most $2\lfloor n/2 \rfloor (n-2)!$ of the vectors obtained by
Externí odkaz:
http://arxiv.org/abs/2002.08535
Autor:
Marberg, Eric, Pawlowski, Brendan
Publikováno v:
Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 273-287
There is a remarkable formula for the principal specialization of a type A Schubert polynomial as a weighted sum over reduced words. Taking appropriate limits transforms this to an identity for the backstable Schubert polynomials recently introduced
Externí odkaz:
http://arxiv.org/abs/2002.00303
Akademický článek
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Publikováno v:
Canad. J. Math. 74 (2022), no. 5, 1310-1346
Involution Schubert polynomials represent cohomology classes of $K$-orbit closures in the complete flag variety, where $K$ is the orthogonal or symplectic group. We show they also represent $T$-equivariant cohomology classes of subvarieties defined b
Externí odkaz:
http://arxiv.org/abs/1911.12009
Let $V_1, V_2, V_3, \dots $ be a sequence of $\mathbb{Q}$-vector spaces where $V_n$ carries an action of $\mathfrak{S}_n$ for each $n$. {\em Representation stability} and {\em multiplicity stability} are two related notions of when the sequence $V_n$
Externí odkaz:
http://arxiv.org/abs/1907.07268
Autor:
Marberg, Eric, Pawlowski, Brendan
Publikováno v:
J. Pure Appl. Algebra 225 (2021), 106463
Grothendieck polynomials, introduced by Lascoux and Sch\"utzenberger, are certain $K$-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the $K$-theory classes of o
Externí odkaz:
http://arxiv.org/abs/1906.01286