Fibonacci numbers and resolutions of domino ideals

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Rachelle R. Bouchat¹  Tricia Muldoon Brown² 

[1] Department of Mathematics, Indiana University of Pennsylvania;Department of Mathematical Sciences, Georgia Southern University

关键词: Fibonacci numbers;    Monomial ideals;    Domino tilings;   

DOI  :  10.13069/jacodesmath.561316

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

This paper considers a class of monomial ideals, called domino ideals, whose generating sets correspondto the sets of domino tilings of a 2 × n tableau. The multi-graded Betti numbers are shown to bein one-to-one correspondence with equivalence classes of sets of tilings. It is well-known that thenumber 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 andthe graded Betti numbers of the corresponding domino ideal.

【 授权许可】

CC BY