Fibonacci numbers and resolutions of domino ideals

Year 2019, Volume: 6 Issue: 2, 63 - 74, 07.05.2019

Rachelle R. Bouchat Tricia Muldoon Brown

https://doi.org/10.13069/jacodesmath.561316

Cited By: 2

Abstract

This paper considers a class of monomial ideals, called domino ideals, whose generating sets correspond to the sets of domino tilings of a $2\times n$ tableau. The multi-graded Betti numbers are shown to be in one-to-one correspondence with equivalence classes of sets of tilings. It is well-known that the number of domino tilings of a $2\times n$ tableau is given by a Fibonacci number. Using the bijection, this relationship is further expanded to show the relationship between the Fibonacci numbers and the graded Betti numbers of the corresponding domino ideal.

Keywords

Fibonacci numbers, Monomial ideals, Domino tilings

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