相关论文: Fibonomial cumulative connection constants

Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…

Combinatorial interpretation of the fibonomial coefficients as a number of choices of specific finite subsets of an infinite partially ordered set of not binomial type is proposed. This partially ordered set is here defined via…

In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…

In this paper, we find several determinants expressing the Fibonomial coefficients. We also give the generating functions, Vandermonde identity, and continued fractions about Fibonomial coefficients.

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…

Roman logarithmic binomial formula analogue has been found . It is presented here also for the case of fibonomial coefficients which recently have been given a combinatorial interpretation by the present author.

We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.

Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.

We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…

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 this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…

We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.

The paper presents several combinatorial properties of the boolean cumulants. A corollary is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted for the case of boolean independence with…

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…

We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…

We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…

We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…

Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…