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arXiv · 2609.26397

Pairs of lattice complements with complementary homology

Sara Faridi·Dharm Veer·Volkmar Welker
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Abstract

In this paper we study whether there is a global to local principle for the homology of order complexes of finite lattices. We explore whether the non-vanishing of the homology of a lattice in degree $a+b-2$ forces the existence of a pair of lattice-complements whose open intervals below have non-vanishing homology in degrees $a$ and $b$ respectively. We consider the same question also in the language of multigraded free resolutions. We provide positive evidence for the existence of such pairs and give counterexamples to strengthenings of the question.

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Sara Faridi, Dharm Veer, Volkmar Welker. 2026-09-22. Pairs of lattice complements with complementary homology. https://arxiv.org/abs/2609.26397

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