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arXiv · 2605.19586

Algebraic aspects of unconditional lattice polytopes

Kenta Mori·Ryo Motomura·Hidefumi Ohsugi·Akiyoshi Tsuchiya
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Abstract

Unconditional polytopes are convex polytopes that are symmetric with respect to all coordinate hyperplanes and arise naturally from anti-blocking polytopes by reflection. This paper investigates algebraic relations between an anti-blocking lattice polytope and its associated unconditional lattice polytope. We prove that the toric ring of an anti-blocking lattice polytope is normal if and only if the toric ring of the associated unconditional lattice polytope is normal. We also show that the toric ideal of an anti-blocking lattice polytope is generated by quadratic binomials if and only if the same holds for the associated unconditional lattice polytope. As an application, we obtain a graph-theoretic characterization of quadratic generation of symmetric stable set ideals.

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Kenta Mori, Ryo Motomura, Hidefumi Ohsugi, Akiyoshi Tsuchiya. 2026-05-19. Algebraic aspects of unconditional lattice polytopes. https://arxiv.org/abs/2605.19586

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