.svg){kind=logo}
GROUPOIDS AND FIBONACCI NUMBERS THROUGH CYCLE COVERS
Keywords:
groupoids, quivers, cycles, permanents, Fibonacci numbersDOI:
https://doi.org/10.17654/0972555525025Abstract
In this article, we characterize some groupoids of Brandt related to Fibonacci numbers. To this end, considering a groupoid G, we compute the number of symmetric subsets having the same cardinality with its unit space. For this computation, we use cycle covers of the quiver associated with G. Finally, we define analogue of toggle maps on these cycle covers.
Received: March 28, 2025
Revised: May 15, 2025
Accepted: May 27, 2025
References
M. Amini, Tannaka-Krein duality for compact groupoids. I. Representation theory, Adv. Math. 214 (2007) 78-91.
I. Assem, D. Simson and A. Skowronski, Elements of the representation theory of associative algebras, 1: techniques of representation theory, London Mathematical Society Student Texts 65, Cambridge University Press, 2006.
K. Atanassov, S. Atanassova, A. Shannon and J. Turner, New Visual Perspectives on Fibonacci Numbers, World Scientific, New Jersey, 2002.
H. Brandt, Idealtheorie in quaternionenalgebren, Math. Ann. 99 (1928) 1-29.
M. Buneci, Groupoid -algebras, Surveys in Math. and its Appl. 1 (2006), 71-98.
O. Cosserat, Symplectic groupoids for Poisson integrators, J. Geom. Phys. 186 (2023), 104751.
R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific, 1997.
J. Feng, Hessenberg matrices on Fibonacci and Tribonacci numbers, Ars Comb. 127 (2016), 117-124.
H. H. Gulec, Permanents and determinants of tridiagonal matrices with -Pell numbers, Int. Math. Forum 12(16) (2017), 747-753.
P. Hahn, Haar measure for measure groupoids, Trans. Amer. Math. Soc. 242 (1978), 1-33.
L. Hogben, ed., Handbook of Linear Algebra, CRC Press, 2006.
Gh. Ivan, Strong morphisms of groupoids, Balkan J. Geom. Appl. 4(1) (1999), 91-102.
M. Joseph and T. Roby, Toggling independent sets of a path graph, Electron. J. Combin. 25(1) (2018), Paper no. 1.18 (31 pages).
K. Kaygisiz and A. Sahin, Determinant and permanent of Hessenberg matrix and Fibonacci type numbers, Gen. 9(2) (2012), 32-41.
K. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Math. Soc., Lectures Notes Series, 124, 1987.
E. K. Magnani and K. Kangni, On a groupoid Gelfand pair, JP Journal of Algebra, Number Theory and Applications 16(2) (2010), 109-118.
Y. Numata and Y. Yamanouchi, On the action of the toggle group of the Dynkin diagram of type Algebraic Combinatorics 5(1) (2022), 149-161.
J. L. Ramirez, Hessenberg matrices and the generalized Fibonacci-Narayana sequence, Filomat 29(7) (2015), 1557-1563.
J. M. Vallin, Groupoides quantiques finis, J. Algebra 239(1) (2001), 215-261.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
