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arXiv · 2308.01365

On $λ$-determinants and tiling problems

Jean-François de Kemmeter·Nicolas Robert·Philippe Ruelle
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Abstract

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

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Jean-François de Kemmeter, Nicolas Robert, Philippe Ruelle. 2023-12-20. On $λ$-determinants and tiling problems. https://doi.org/10.1088/1751-8121%2Fad0fb2

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