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arXiv · 2505.14800

Exploring the Varchenko Determinant of Partial Cubes

Winfried Hochstättler·Sophia Keip·Birol Yazici
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Abstract

The Varchenko matrix is known to have a well-structured determinant for complexes of oriented matroids (COMs). COMs can be characterized as partial cubes that do not have certain forbidden pc-minors. In this work, we generalize the Varchenko matrix and its determinant to partial cubes. We identify examples of partial cubes whose Varchenko determinants lack a clean factorization, as well as those that exhibit such a structure. These findings open the door for further research into the properties and potential characterizations of partial cubes with well-behaved Varchenko determinants.

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Winfried Hochstättler, Sophia Keip, Birol Yazici. 2025-05-20. Exploring the Varchenko Determinant of Partial Cubes. https://arxiv.org/abs/2505.14800

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