Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Konvalinka, Matjaz"'
Autor:
Billey, Sara, Konvalinka, Matjaž
In this paper, we present new objects, quilts of alternating sign matrices with respect to two given posets. Quilts generalize several commonly used concepts in mathematics. For example, the rank function on submatrices of a matrix gives rise to a qu
Externí odkaz:
http://arxiv.org/abs/2412.03236
We study the action of $S_n$ on the set of break divisors on complete multigraphs $K_{n}^m$. We provide an alternative characterization for these divisors, by virtue of which we show that orbits of this action are enumerated by the numerical Donaldso
Externí odkaz:
http://arxiv.org/abs/2111.07071
We study the Schur polynomial expansion of a family of symmetric polynomials related to the refined enumeration of alternating sign matrices with respect to their inversion number, complementary inversion number and the position of the unique $1$ in
Externí odkaz:
http://arxiv.org/abs/2005.12448
The study of permutation and partition statistics is a classical topic in enumerative combinatorics. The major index statistic on permutations was introduced a century ago by Percy MacMahon in his seminal works. In this extended abstract, we study th
Externí odkaz:
http://arxiv.org/abs/2005.10341
Berget and Rhoades asked whether the permutation representation obtained by the action of $S_{n-1}$ on parking functions of length $n-1$ can be extended to a permutation action of $S_{n}$. We answer this question in the affirmative. We realize our mo
Externí odkaz:
http://arxiv.org/abs/2004.12093
Autor:
Konvalinka, Matjaž, Tewari, Vasu
We construct a family of $S_n$ modules indexed by $c\in\{1,\dots,n\}$ with the property that upon restriction to $S_{n-1}$ they recover the classical parking function representation of Haiman. The construction of these modules relies on an $S_n$-acti
Externí odkaz:
http://arxiv.org/abs/2003.04134
Autor:
Fischer, Ilse, Konvalinka, Matjaž
This paper is the second in a series of planned papers which provide first bijective proofs of alternating sign matrix results. Based on the main result from the first paper, we construct a bijective proof of the enumeration formula for alternating s
Externí odkaz:
http://arxiv.org/abs/1912.01354
Autor:
Fischer, Ilse, Konvalinka, Matjaz
Alternating sign matrices are known to be equinumerous with descending plane partitions, totally symmetric self-complementary plane partitions and alternating sign triangles, but no bijective proof for any of these equivalences has been found so far.
Externí odkaz:
http://arxiv.org/abs/1910.04198
We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary statistic, a
Externí odkaz:
http://arxiv.org/abs/1905.00975
Autor:
Konvalinka, Matjaž, Tewari, Vasu
We introduce a generalization of Smirnov words in the context of labeled binary trees, which we call Smirnov trees. We study the generating function for ascent-descent statistics on Smirnov trees and establish that it is $e$-positive, which is akin t
Externí odkaz:
http://arxiv.org/abs/1901.10140