Elliptic and q-analogs of the Fibonomial numbers

Cesar Ceballos; Nantel Bergeron; Josef Küstner

doi:10.3842/SIGMA.2020.076

Elliptic and q-analogs of the Fibonomial numbers

Cesar Ceballos , Nantel Bergeron, Josef Küstner^*

^*Corresponding author for this work

Institute of Geometry (5070)

Research output: Contribution to journal › Article › peer-review

Abstract

In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In this paper, we present a combinatorial description for the q-analog and elliptic analog of the Fibonomial numbers. This is achieved by introducing some q-weights and elliptic weights to a slight modification of the combinatorial model of Sagan and Savage.

Original language	English
Article number	076
Pages (from-to)	1-16
Number of pages	16
Journal	Symmetry, Integrability and Geometry: Methods and Applications
Volume	16
DOIs	https://doi.org/10.3842/SIGMA.2020.076
Publication status	Published - 13 Aug 2020

Keywords

Elliptic analog
Fibonacci
Fibonomial
Q-analog
Weighted enumeration

ASJC Scopus subject areas

Analysis
Geometry and Topology
Mathematical Physics

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https://www.emis.de/journals/SIGMA/2020/076/sigma20-076.pdfLicence: CC BY-SA 4.0

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author = "Cesar Ceballos and Nantel Bergeron and Josef K{\"u}stner",

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AB - In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In this paper, we present a combinatorial description for the q-analog and elliptic analog of the Fibonomial numbers. This is achieved by introducing some q-weights and elliptic weights to a slight modification of the combinatorial model of Sagan and Savage.

KW - Elliptic analog

KW - Fibonacci

KW - Fibonomial

KW - Q-analog

KW - Weighted enumeration

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Elliptic and q-analogs of the Fibonomial numbers

Abstract

Keywords

ASJC Scopus subject areas

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