Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations

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Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations

Koutschan, C.; Krattenthaler, C.; Schlosser, M.J.

Journal of symbolic computation, March-April 2025, 2025-03-00, Volume: 127

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In his work on the twenty vertex model, Di Francesco (2021) 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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Koutschan, C. | Krattenthaler, C. | Schlosser, M.J.

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