Tridendriform algebras on hypergraph polytopes, the other way around

Pierre-Louis Curien; Bérénice Delcroix-Oger; Jovana Obradović

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arXiv · 2606.17755

Tridendriform algebras on hypergraph polytopes, the other way around

Pierre-Louis Curien·Bérénice Delcroix-Oger·Jovana Obradović

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Abstract

Hypergraph polytopes (or nestohedra) form a broad class of polytopes obtained by truncating faces of a simplex according to a hypergraph. In earlier work, the authors constructed q-tridendriform algebras on the set of faces of certain families of hypergraph polytopes, including associahedra and permutohedra. The well-definedness of these structures relied on a connectedness property on the hypergraphs involved, called strictness. Nevertheless, notable examples of hypergraph polytopes such as cyclohedra fell outside this setting. We introduce a new connectedness condition, called anti-strictness, which goes opposite to strictness and captures a different class of hypergraph polytopes, including associahedra, permutohedra and cyclohedra. Our main result produces natural (-1)-tridendriform algebras in the anti-strict framework, which match previously introduced tridendriform algebras in the overlap of the two frameworks, thereby extending the range of hypergraph polytopes admitting such algebraic structures.

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Pierre-Louis Curien, Bérénice Delcroix-Oger, Jovana Obradović. 2026-08-21. Tridendriform algebras on hypergraph polytopes, the other way around. https://arxiv.org/abs/2606.17755

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