On $\lambda$-determinants and tiling problems
Mathematical Physics
2023-12-21 v2 Statistical Mechanics
Combinatorics
math.MP
Abstract
We review the connections between the octahedral recurrence, -determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the -determinant (and generalizations thereof) of an arbitrary matrix in terms of domino tilings of Aztec diamonds. We also reinterpret the general Robbins-Rumsey formula for the rational function of consecutive minors, given by a summation over pairs of compatible alternating sign matrices, as the partition function for tilings of Aztec diamonds equipped with a general measure.
Cite
@article{arxiv.2308.01365,
title = {On $\lambda$-determinants and tiling problems},
author = {Jean-François de Kemmeter and Nicolas Robert and Philippe Ruelle},
journal= {arXiv preprint arXiv:2308.01365},
year = {2023}
}
Comments
31 pages, published version; v2 slightly augmented with relations to Somos-4 sequences (see end of section 3.2 and appendix)