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Year 2019, Volume 6 , Issue 2, Pages 63 - 74 2019-05-07

Fibonacci numbers and resolutions of domino ideals

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

Abstract

This paper considers a class of monomial ideals, called domino ideals, whose generating sets correspond to the sets of domino tilings of a $2\times n$ 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.

Keywords

Fibonacci numbers, Monomial ideals, Domino tilings

References

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Details

Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0003-2286-0805
Author: Rachelle R. BOUCHAT

Orcid: 0000-0003-3835-1175
Author: Tricia Muldoon BROWN (Primary Author)
Dates

Publication Date : May 7, 2019

Cite

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 <https://dergipark.org.tr/en/pub/jacodesmath/article/561316>
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
Rachelle R. BOUCHAT [1]
Tricia Muldoon BROWN [2]
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