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arXiv · 2605.23849

Incidence toric ideals and three-point functions

Barbara Betti·Sean Grate·Thiago Holleben·Flavio Salizzoni
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Abstract

We study the ideal of the algebraic relations among 3-point functions from a combinatorial and topological perspective. We place this problem in the broader setting of incidence toric ideals associated with incidence matrices of t-subsets contained in k-subsets of n elements. Generators of these ideals admit combinatorial interpretations as null t-designs and topological interpretations as balanced orientable normal d-pseudomanifolds without boundary. Generators arising from octahedra play a fundamental role in the structure of these ideals.

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Barbara Betti, Sean Grate, Thiago Holleben, Flavio Salizzoni. 2026-05-22. Incidence toric ideals and three-point functions. https://arxiv.org/abs/2605.23849

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