相关论文: Fibonomial determinants
In this paper, we show combinatorial identities that represent powers of positive integers using multinomial coefficients, which do not come from the multinomial theorem and the multinomial Vandermonde's convolution.
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici \`a…
In response to [6], we discover the looked for inversion formula for F-nomial coefficients. Before supplying its proof, we generalize F-nomial coefficients to multi F-nomial coefficients and we give their combinatorial interpretation in…
A compound determinant identity for minors of rectangular matrices is established. As an application, we derive Vandermonde type determinant formulae for classical group characters.
Explicit expressions are proven for derivatives of the ratio of a determinant or Pfaffian determinant and a Vandermonde determinant. Such ratios appear for example in general group integrals of Harish-Chandra--Itzykson--Zuber type and in…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and…
In this paper, we introduce the Tribonacci and Tribonacci-Lucas quaternion polynomials. We obtain the Binet formulas, generating functions and exponential generating functions of these quaternions. Moreover, we give some properties and…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.
In this paper, we will obtain a variety of interesting $q$-series containing central $q$-binomial coefficients. Our approach is based on manipulating deformed basic hypergeometric series.
We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the…
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into…
The golden binomials, introduced in the golden quantum calculus, have expansion determined by Fibonomial coefficients and the set of simple zeros given by powers of Golden ratio. We show that these golden binomials are equivalent to Carlitz…
We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.
In this article, we will discover some new generalized identity regarding continued fractions. We will connect the results to Fibonacci numbers and Lucas numbers. For all the proof, we will use induction.
In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
The middle binomial coefficients can be interpreted as numbers of Motzkin paths which have no horizontal steps at positive heights. Assigning suitable weights gives some nice polynomial extensions. We determine the Hankel determinants and…
In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are…
In this paper, we give some determinantal and permanental representations of Generalized Fibonacci Polynomials by using various Hessenberg matrices. These results are general form of determinantal and permanental representations of k…