Related papers: A generalization of complete and elementary symmet…

We give an elementary symmetric function expansion for $M\Delta_{m_\gamma e_1}\Pi e_\lambda^{\ast}$ and $M\Delta_{m_\gamma e_1}\Pi s_\lambda^{\ast}$ when $t=1$ in terms of what we call $\gamma$-parking functions and lattice $\gamma$-parking…

In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…

The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…

The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the generating function. we unify all forms of q-exponential functions by one more parameter. we…

We use actions by finite cyclic groups to derive generalizations of three classical theorems from elementary number theory.

This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…

We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…

There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences,…

The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…

First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…

This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties…

We prove that, under certain assumptions, generalized Hilbert-Kunz multiplicities can be expressed as linear combinations of classical Hilbert-Kunz multiplicities.

Properties of the four families of recently introduced special functions of two real variables, denoted here by $E^\pm$, and $\cos^\pm$, are studied. The superscripts $^+$ and $^-$ refer to the symmetric and antisymmetric functions…

This paper is about a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials. We introduce two sets of (skew and non-skew) functions that are akin to P and Q…

In this paper, using the theory of category, we generalize known properties of symmetric polynomials and functions and characterize the multi-indicial symmetric functions. Examples have been given on Schur functions.

In our previous works we introduced a $q$-deformation of the generating functions for enriched $P$-partitions. We call the evaluation of this generating functions on labelled chains, the $q$-fundamental quasisymmetric functions. These…

From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…

By using exclusively real analysis, we give explicit estimates of some classical summatory functions involving the M\"obius function.

We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…

We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…