Related papers: On Characteristic Polynomials of the Family of Cob…

Kwasniewski's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation…

A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…

Following Lucas and then other Fibonacci people Kwasniewski had introduced and had started ten years ago the open investigation of the overall F-nomial coefficients which encompass among others Binomial, Gaussian and Fibonomial coefficients…

Cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation was derived in…

We use the characteristic polynomial of the Coxeter matrix of an algebra to complete the combinatorial classification of piecewise hereditary algebras which Happel gave in terms of the trace of the Coxeter matrix. We also give a…

We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…

Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.

The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. It has been a challenging open problem to determine which posets have real-rooted chain polynomials. Two new classes of…

We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…

The characteristic polynomial plays an important role in study of hyperplane arrangements. There are several refinements of the characteristic polynomial. One of them is the coboundary polynomial defined by Crapo. Another refinement is the…

In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers…

The explicite formulas for Mobius function and some other important elements of the incidence algebra of an arbitrary cobweb poset are delivered. For that to do one uses Kwasniewski's construction of his cobweb posets . The digraph…

In this paper, certain mixed special polynomial families associated with Appell sequences are introduced and their properties are established. Further, operational rules providing connections between these families and the known special…

Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…

The main purpose of this article is to pose three problems which are easy to be formulated in an elementary way. These problems which are specifically important also for the new class of partially ordered sets seem to be not yet solved.

This paper addresses the topic of equidistribution and recurrence for polynomial sequences over function fields. The main focus is to note and correct two small errors in [V. Bergelson and A. Leibman, A Weyl-type equidistribution theorem in…

Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates the numbers of elements in the complement of hyperplane arrangements modulo positive integers. In this paper, we compute the characteristic…

In this paper, the correspondence between the finite dimensional representations of a simple Lie algebra and their characteristic polynomials is established, and a monoid structure on these characteristic polynomials is constructed.…

An equivariant characteristic quasi-polynomial is a quasi-polynomial in $q$ consisting of the permutation character on the mod $q$ complement of the corresponding Coxeter arrangement. This concept is a refinement of the conventional…

A class of new type graded infinite posets with minimal element are considered. These so called cobweb posets introduced recently by the present author provide a wide range of new noncommutative prefab combinatorial schema with…