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

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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.

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Authors and Affiliations

  1. St. Petesburg Department of Mathematics Institute, St. Petersburg, Russia

    I. N. Burenev

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  1. I. N. Burenev
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Correspondence to I. N. Burenev.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 509, 2021, pp. 71–88.

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Burenev, I.N. Five-Vertex Model and Lozenge Tilings of a Hexagon with a Dent. J Math Sci 275, 271–282 (2023). https://doi.org/10.1007/s10958-023-06679-5

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  • DOI: https://doi.org/10.1007/s10958-023-06679-5

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