Elliptic and q-analogs of the Fibonomial numbers
Welcome! This is the website of the FPSAC 2020 poster on "Elliptic and q-analogs of the Fibonomial numbers" by Nantel Bergeron, Cesar Ceballos, and Josef Küstner.
The poster:
PDF
More details on:
q-Fibonacci analog of the Coxeter Catalan numbers
Elliptic Fibonomial numbers
Our poster as a small section of the map of Fibonacci World:
prezi.com/view/Hu6hnUmsRbExsmBi5HBW/
You can find our paper as a preprint here:
arxiv.org/abs/1911.12785
Slides from a talk by J.K. in Strobl 2019:
PDF
Abstract
In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefcients 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.
Further reading
More on Fibonomials and related content
The model for Fibonomials (and Lucasnomials) by Bruce Sagan and Carla Savage we are generlizing:
arxiv.org/abs/0911.3159
A very interesting new model for Fibonomials and Lucasnomials by Curtis Bennett, Juan Carrillo, John Machacek, and Bruce Sagan with nice applications:
arxiv.org/abs/1809.09036
"Lucas atoms" - a powerful algebraic method to find out whether Lucas (and Fibonacci) analogs are polynomials. By Bruce Sagan and Jordan Tirrell:
arxiv.org/abs/1909.02593
Combinatorial interpretations of Fibonomial identities by Arthur T. Benjamin and Elizabeth Reiland:
fq.math.ca/Papers1/52-5/Benjamin.pdf
Fundamental properties of Fibonacci polynomials and Fibonomials by Tewodros Amdeberhan, Xi Chen, Victor H. Moll, and Bruce Sagan:
arxiv.org/abs/1306.6511
Some more elliptic analogs
Elliptic enumeration of nonintersacting lattice paths by Michael Schlosser:
mat.univie.ac.at/~schlosse/ellpaths.html
Weighted enumeration of plane partitions by Alexei Borodin, Vadim Gorin, and Eric M. Rains:
arxiv.org/abs/0905.0679
Elliptically Distributed Lozenge Tilings of a Hexagon by Dan Batea:
arxiv.org/abs/1110.4176
Elliptic rook and file numbers by Michael Schlosser and Meesue Yoo:
arxiv.org/abs/1512.01720v3