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Communications in Algebra Volume 50, 2022 - Issue 5
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Articles

Multigraded Betti numbers of Möbius domino ideals

Rachelle R. Bouchata Department of Mathematical and Computer Sciences, Indiana University of Pennsylvania, Indiana, Pennsylvania, USA;b Mathematics Department, Berea College, Berea, Kentucky, USA
&
Tricia Muldoon Brownc Department of Mathematical Sciences, Georgia Southern University, Savannah, Georgia, USACorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0003-3835-1175
ORCID Icon
Pages 2269-2278 | Received 28 Jan 2021, Accepted 06 Nov 2021, Published online: 29 Nov 2021
 
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Abstract

We enumerate graded Betti numbers of the minimal free resolutions of ideals generated by domino tilings of 2×n Möbius bands by using combinatorial information from the domino tilings in two ways: first using a splitting function to find a recursive formula and second using a bijection to enumerate in terms of binomial coefficients and Fibonacci numbers.

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