Gaussian Binomial Coefficients with Negative Arguments
نویسندگان
چکیده
منابع مشابه
Projective Geometry over and the Gaussian Binomial Coefficients
1. INTRODUCTION. There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and algebra, but it is rarely discussed as such. The purpose of this article is to bring it to the attention of a broader audience, as the solution to ...
متن کاملOn the q - log - Concavity of Gaussian Binomial Coefficients 335
We give a combinatorial proof that k l-k-1 l + t q q q q a polynomial in q with nonnegative coefficients for nonnegative integers a, b, k, lwith a>~b and l~>k. In particular, for a=b=n and l=k, this implies the q-log-concavity of the Gaussian binomial coefficients k , which was conjectured q by BUTLER (Proc.
متن کاملGeometry of Binomial Coefficients
This note describes the geometrical pattern of zeroes and ones obtained by reducing modulo two each element of Pascal's triangle formed from binomial coefficients. When an infinite number of rows of Pascal's triangle are included, the limiting pattern is found to be "self-similar," and is characterized by a "fractal dimension" log2 3. Analysis of the pattern provides a simple derivation of the ...
متن کاملIdentities with squares of binomial coefficients
This paper introduces a method for finding closed forms for certain sums involving squares of binomial coefficients. We use this method to present an alternative approach to a problem of evaluating a different type of sums containing squares of the numbers from Catalan's triangle.
متن کاملEVALUATION OF SUMS INVOLVING GAUSSIAN q-BINOMIAL COEFFICIENTS WITH RATIONAL WEIGHT FUNCTIONS
We consider sums of the Gaussian q-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications of our results to certain generalized Fibonomial sums weighted with finite products of reciprocal Fibonacci or Lucas numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2019
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-019-00472-5