Connection between bi$^{s}$nomial coefficients and their analogs and symmetric functions

Authors

ABDELGHAFOUR BAZENIAR
MOUSSA AHMIA
HACENE BELBACHIR

Abstract

In this paper, on one hand, we propose a new type of symmetric function to interpret the bi$^{s}$nomial coefficients and their analogs. On other hand, according to this function, we give an interpretation of these coefficients by lattice paths and tiling. Some identities of these coefficients are also established. This work is an extension of the results of Belbachir and Benmezai's ''A $\mathit{q}$-analogue for bi$^{\mathit{s}}$nomial coefficients and generalized Fibonacci sequences".

DOI

10.3906/mat-1705-27

Keywords

Bi$^{s}$nomial coefficients, symmetric functions, lattice paths, tiling

First Page

807

Last Page

818

Recommended Citation

BAZENIAR, ABDELGHAFOUR; AHMIA, MOUSSA; and BELBACHIR, HACENE (2018) "Connection between bi$^{s}$nomial coefficients and their analogs and symmetric functions," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 7. https://doi.org/10.3906/mat-1705-27
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/7