Determinant evaluations inspired by Di Francesco's determinant
for twenty-vertex configurations
(35 pages)
Abstract.
In his work on the twenty vertex model, Di Francesco
[Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a
determinant formula for the number of configurations in a specific
such model, and he conjectured a closed form product formula for the
evaluation of this determinant. We prove this conjecture here.
Moreover, we actually generalize this determinant evaluation to a
one-parameter family of determinant evaluations, and we present
many more determinant evaluations of similar type - some proved,
some left open as conjectures.
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