Five-Vertex Model and Lozenge Tilings of a Hexagon with a Dent

We consider the five-vertex model on a regular square lattice of the size L × M with boundary conditions fixed in such a way that configurations of the model are in one-to-one correspondence with the lozenge tilings of the hexagon with a dent. We obtain two determinant representations for the partit...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-09, Vol.275 (3), p.271-282
Main Author: Burenev, I. N.
Format: Article
Language:English
Subjects:
Boundary conditions
Mathematics
Mathematics and Statistics
Partitions (mathematics)
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Summary:We consider the five-vertex model on a regular square lattice of the size L × M with boundary conditions fixed in such a way that configurations of the model are in one-to-one correspondence with the lozenge tilings of the hexagon with a dent. We obtain two determinant representations for the partition function. In the free-fermionic limit, this result implies some summation formulae for Schur functions.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06679-5