Fibonacci numbers and resolutions of domino ideals

Rachelle R. Bouchat, Tricia Muldoon Brown

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 × 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.

Original languageEnglish
Pages (from-to)63-67
Number of pages5
JournalJournal of Algebra Combinatorics Discrete Structures and Applications
Volume6
Issue number2
DOIs
StatePublished - 2019

Scopus Subject Areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

Keywords

  • Domino tilings
  • Fibonacci numbers
  • Monomial ideals

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