A classification of van der Waerden complexes with linear resolution
DOI:
https://doi.org/10.7146/math.scand.a-157260Abstract
In 2017, Ehrenborg, Govindaiah, Park, and Readdy defined the van der Waerden complex $\mathsf{vdW}(n,k)$ to be the simplicial complex whose facets correspond to all the arithmetic sequences on the set $\{1,\ldots,n\}$ of a fixed length $k$. To complement a classification of the Cohen–Macaulay van der Waerden complexes obtained by Hooper and Van Tuyl in 2019, a classification of van der Waerden complexes with linear resolution is presented. Furthermore, we show that the Stanley–Reisner ring of a Cohen–Macaulay van der Waerden complex is level.
References
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Hooper, B., and Van Tuyl, A., A note on the van der Waerden complex, Math. Scand. 124 (2019), no. 2, 179–187. https://doi.org/10.7146/math.scand.a-111923
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