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pro vyhledávání: '"05E05, 05E15"'
Autor:
Brini, Andrea, Teolis, Antonio
In this paper are introduced two classes of elements in the enveloping algebra $\mathbf{U}(gl(n))$: the \emph{double Young-Capelli bitableaux} $[\ \fbox{$S \ | \ T$}\ ]$ and the \emph{central} \emph{Schur elements} $\mathbf{S}_{\lambda}(n)$, that act
Externí odkaz:
http://arxiv.org/abs/2107.10205
Publikováno v:
Adv. Appl. Math. 121 (2020), 102080
We study the symmetric function and polynomial combinatorial invariants of Hopf algebras of permutations, posets and graphs. We investigate their properties and the relations among them. In particular, we show that the chromatic symmetric function an
Externí odkaz:
http://arxiv.org/abs/1908.04841
Autor:
Brini, Andrea, Teolis, Antonio
We propose a new approach to a unified study of determinants, permanents, immanants, (determinantal) bitableaux and symmetrized bitableaux in the polynomial algebra $C[M_{n, n}]$ as well as of their Lie analogues in the enveloping algebra $U(gl(n))$.
Externí odkaz:
http://arxiv.org/abs/1807.10045
Publikováno v:
J. Combin. Theory Ser. A 161: 420--452 (2019)
We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard augmented fillings studied by Haglund, Mason and Remmel. Our primary moti
Externí odkaz:
http://arxiv.org/abs/1712.05008
Autor:
Zhang, Zerui, Chen, Yuqun
By applying a Gr\"{o}bner-Shirshov basis of the symmetric group $S_{n}$, we give two formulas for Schubert polynomials, either of which involves only nonnegative monomials. We also prove some combinatorial properties of Schubert polynomials. As appli
Externí odkaz:
http://arxiv.org/abs/1705.08069
Autor:
Kosuda, Masashi, Oura, Manabu
The purpose of this paper is to investigate the finite group which appears in the study of the Type II $\mathbf{Z}_4$-codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the centralizer al
Externí odkaz:
http://arxiv.org/abs/1608.08731
Autor:
Blasiak, Jonah, Fomin, Sergey
We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of elements of a ring labeled by any subset of indices, it is enough that
Externí odkaz:
http://arxiv.org/abs/1608.05042
We define an analog of David Little's algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algorithm preserves the recording tableau of Kra\'{s}kiewicz insertion, and that it provides a bijective
Externí odkaz:
http://arxiv.org/abs/1405.4891
Autor:
Pon, Steven
We introduce affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the special linear
Externí odkaz:
http://arxiv.org/abs/1111.3312
A compound determinant identity for minors of rectangular matrices is established. As an application, we derive Vandermonde type determinant formulae for classical group characters.
Comment: 22 pages
Comment: 22 pages
Externí odkaz:
http://arxiv.org/abs/1106.2915