𝔖 Bobbio Scriptorium
✦   LIBER   ✦

q-generalization of a ballot problem

✍ Scribed by C. Krattenthaler; S.G. Mohanty

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
721 KB
Volume
126
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

n-dimensional lattice paths which do not touch the hyperplanes xi-xi + I = -1, i = 1,2, , n -1, and x,-x1 = -1 -K arc enumerated by certain statistics, one of which is MacMahon's major index, the others being variations of it. By a reflection-like proof, a formula involving determinants is obtained. It is a q-extension of Filaseta's (1985) expression for the number of elections in a specific ballot problem.

πŸ“œ SIMILAR VOLUMES

A generalization of Q-admissibility
A generalization of Q-admissibility
✍ Burton Fein; Murray Schacher πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 887 KB
A generalization of the Oberwolfach prob
A generalization of the Oberwolfach problem
✍ S. I. El-Zanati; S. K. Tipnis; C. Vanden Eynden πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 117 KB

## Abstract Let __n__ > 1 be an integer and let __a__~2~,__a__~3~,…,__a__~__n__~ be nonnegative integers such that $\sum\_{i=2}^{n} a\_i=2^{n-1} - 1$. Then $K\_{2^n}$ can be factored into $a\_2 C\_{2^2}$‐factors, $a\_3 C\_{2^3}$‐factors,…,$a\_n C\_{2^n}$‐factors, plus a 1‐factor. Β© 2002 Wiley Perio

A Generalization of Two q-Identities of
A Generalization of Two q-Identities of Andrews
✍ Kuo-Jye Chen; H.M. Srivastava πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 87 KB

The main object of the present paper is to give a unification (and generalization) of two interesting q-identities which were proven recently by George E. Andrews. Some related results involving the Fibonacci numbers are also considered. 2001