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arXiv · 1708.07054

Minimal Free Resolutions of $2\times n$ Domino Tilings

Rachelle R. Bouchat·Tricia Muldoon Brown
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Abstract

We introduce a squarefree monomial ideal associated to the set of domino tilings of a $2\times n$ rectangle and proceed to study the associated minimal free resolution. In this paper, we use results of Dalili and Kummini to show that the Betti numbers of the ideal are independent of the underlying characteristic of the field, and apply a natural splitting to explicitly determine the projective dimension and Castelnuovo-Mumford regularity of the ideal.

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Rachelle R. Bouchat, Tricia Muldoon Brown. 2017-08-23. Minimal Free Resolutions of $2\times n$ Domino Tilings. https://doi.org/10.1142/s0219498819501184

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