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 language | English |
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Pages (from-to) | 63-67 |
Number of pages | 5 |
Journal | Journal of Algebra Combinatorics Discrete Structures and Applications |
Volume | 6 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Scopus Subject Areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics
Keywords
- Domino tilings
- Fibonacci numbers
- Monomial ideals