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arXiv · 2602.21907

Betti numbers of skeletons of thick trees

Ralf Fröberg
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Abstract

The starting point is the class of the following simplicial complexes $\Delta$ with 2-linear resolutions. The facets of $\Delta$ are $F_1,\ldots,F_n$, and we demand that for each $i$ $F_i\cap (F_1\cup \cdots\cup F_{i-1}\cup F_{i+1}\cdots\cup F_n)$ be a point. We will determine the Betti numbers, and thus the projective dimension, the depth, and the regularity of the Stanley-Reisner rings of all skeletons of such complexes. It follows that we know when these complexes are Cohen-Macaulay. Also, there are two ways to determine the Hilbert series of $\Delta$, giving sequences of identities for binomial coefficients.

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Ralf Fröberg. 2026-02-25. Betti numbers of skeletons of thick trees. https://arxiv.org/abs/2602.21907

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