Geodesic
Five-vertex model and lozenge tilings of a hexagon with a dent
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 71-88

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We consider the five-vertex model on a regular square lattice of the size $L \times M$ 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. 
@article{ZNSL_2021_509_a4,
     author = {I. N. Burenev},
     title = {Five-vertex model and lozenge tilings of a hexagon with a dent},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {71--88},
     publisher = {mathdoc},
     volume = {509},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a4/}
}
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I. N. Burenev. Five-vertex model and lozenge tilings of a hexagon with a dent. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 71-88. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a4/