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arXiv · 2401.08481

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

Christoph Koutschan·Christian Krattenthaler·Michael Schlosser
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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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Christoph Koutschan, Christian Krattenthaler, Michael Schlosser. 2024-01-16. Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations. https://arxiv.org/abs/2401.08481

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