相关论文: Combinatorial interpretation of the coefficients o…
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…
We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.
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…
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
Recently a definition for a Lorentz invariant operator approximating the d'Alembertian in d-dimensional causal set space-times has been proposed. This operator contains several dimension-dependent constants which have been determined for…
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
We define and study the combinatorial properties of compositional Bernoulli numbers and polynomials within the framework of rational combinatorics.
Meta-analysis is commonly used to combine results from multiple clinical trials, but traditional meta-analysis methods do not refer explicitly to a population of individuals to whom the results apply and it is not clear how to use their…
In this paper we shall evaluate two alternating sums of binomial coefficients by a combinatorial argument. Moreover, by combining the same combinatorial idea with partition theoretic techniques, we provide $q$-analogues involving the…
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on…
An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…
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…
Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
New criterion of regularity for representation of canonical commutation relations algebra is given on the basis of concept of an analytical vector.
A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and…
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
Kerov's polynomials give irreducible character values in term of the free cumulants of the associated Young diagram. We prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. Our method,…
In the paper, the authors analytically generalize the Catalan numbers in combinatorial number theory, establish an integral representation of the analytic generalization of the Catalan numbers by virtue of Cauchy's integral formula in the…
A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory…