7 research outputs found
Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity
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