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## Fibonacci numbers and resolutions of domino ideals

#### Rachelle R. BOUCHAT [1] , Tricia Muldoon BROWN [2]

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.
Fibonacci numbers, Monomial ideals, Domino tilings
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Primary Language en Engineering Articles Orcid: 0000-0003-2286-0805Author: Rachelle R. BOUCHAT Orcid: 0000-0003-3835-1175Author: Tricia Muldoon BROWN (Primary Author) Publication Date : May 7, 2019
 Bibtex @research article { jacodesmath561316, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2019}, pages = {63 - 74}, doi = {10.13069/jacodesmath.561316}, title = {Fibonacci numbers and resolutions of domino ideals}, key = {cite}, author = {Bouchat, Rachelle R. and Brown, Tricia Muldoon} } APA Bouchat, R , Brown, T . (2019). Fibonacci numbers and resolutions of domino ideals . Journal of Algebra Combinatorics Discrete Structures and Applications , 6 (2) , 63-74 . DOI: 10.13069/jacodesmath.561316 MLA Bouchat, R , Brown, T . "Fibonacci numbers and resolutions of domino ideals" . Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 63-74 Chicago Bouchat, R , Brown, T . "Fibonacci numbers and resolutions of domino ideals". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 63-74 RIS TY - JOUR T1 - Fibonacci numbers and resolutions of domino ideals AU - Rachelle R. Bouchat , Tricia Muldoon Brown Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.561316 DO - 10.13069/jacodesmath.561316 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 63 EP - 74 VL - 6 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.561316 UR - https://doi.org/10.13069/jacodesmath.561316 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Fibonacci numbers and resolutions of domino ideals %A Rachelle R. Bouchat , Tricia Muldoon Brown %T Fibonacci numbers and resolutions of domino ideals %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 2 %R doi: 10.13069/jacodesmath.561316 %U 10.13069/jacodesmath.561316 ISNAD Bouchat, Rachelle R. , Brown, Tricia Muldoon . "Fibonacci numbers and resolutions of domino ideals". Journal of Algebra Combinatorics Discrete Structures and Applications 6 / 2 (May 2019): 63-74 . https://doi.org/10.13069/jacodesmath.561316 AMA Bouchat R , Brown T . Fibonacci numbers and resolutions of domino ideals. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 63-74. Vancouver Bouchat R , Brown T . Fibonacci numbers and resolutions of domino ideals. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(2): 63-74. IEEE R. Bouchat and T. Brown , "Fibonacci numbers and resolutions of domino ideals", Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 2, pp. 63-74, May. 2019, doi:10.13069/jacodesmath.561316

Authors of the Article
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