On λ-determinants and tiling problems
(2024) Journal of Physics A: Mathematical and Theoretical — Vol. 57, n° 1, p. 15209 (2024)
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- Authors
de Kemmeter, Jean-François 
- 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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Citations
de Kemmeter, J.-F., Robert, N., & Ruelle, P. (2024). On λ-determinants and tiling problems. Journal of Physics A: Mathematical and Theoretical, 57(1), 15209. https://doi.org/10.1088/1751-8121/ad0fb2 (Original work published 2024)