Minimal free resolutions of 2 × n domino tilings

Bouchat, Rachelle R.; Brown, Tricia Muldoon

doi:10.1142/s0219498819501184

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“…These results, among others, suggest that interpretation as monomial ideals will also be of interest. Here, we extend previous work by the authors [6] to enumerative results concerning the multi-graded and graded Betti numbers of the ideal corresponding to the set of all 2 × n domino tilings.…”

Section: Introductionsupporting

confidence: 63%

Fibonacci numbers and resolutions of domino ideals

Bouchat¹,

Brown²

2019

Journal of Algebra Combinatorics Discrete Structures and Applications

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This paper considers a class of monomial ideals, called domino ideals, whose generating sets correspond to the sets of domino tilings of a 2 × 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 × 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.2010 MSC: 05E40, 13A15

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Section: Introductionsupporting

confidence: 63%