In 2007, the first author gave an alternative proof of the refined alternating sign matrix theorem by introducing a linear equation system that determines the refined ASM numbers uniquely. Computer experiments suggest that the numbers appearing in a conjecture concerning the number of vertically symmetric alternating sign matrices with respect to the position of the first 1 in the second row of the matrix establish the solution of a linear equation system similar to the one for the ordinary refined ASM numbers. In this paper we show how our attempt to prove this fact naturally leads to a more general conjectural multivariate Laurent polynomial identity. Remarkably, in contrast to the ordinary refined ASM numbers, we need to extend the combinatorial interpretation of the numbers to parameters which are not contained in the combinatorial admissible domain. Some partial results towards proving the conjectured multivariate Laurent polynomial identity and additional motivation why to study it are presented as well.
@article{10_37236_4436,
author = {Ilse Fischer and Lukas Riegler},
title = {Vertically symmetric alternating sign matrices and a multivariate {Laurent} polynomial identity},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4436},
zbl = {1305.05031},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4436/}
}
TY - JOUR
AU - Ilse Fischer
AU - Lukas Riegler
TI - Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4436/
DO - 10.37236/4436
ID - 10_37236_4436
ER -
%0 Journal Article
%A Ilse Fischer
%A Lukas Riegler
%T Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4436/
%R 10.37236/4436
%F 10_37236_4436
Ilse Fischer; Lukas Riegler. Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4436
