On $\lambda$-determinants and tiling problems

Abstract

We review the connections between the octahedral recurrence, $\lambda$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $\lambda$-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.

31 pages, published version; v2 slightly augmented with relations to Somos-4 sequences (see end of section 3.2 and appendix)

References in corpus (2)

• On the domino shuffle and matrix refactorizations
• Double tangent method for two-periodic Aztec diamonds