Related papers: On sequences preserving summability
In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize…
In this note, we show the existence of integer sequences of lengths at least 3 (except 7) such that for every integer in position $i\equiv 1\pmod{4}$ (respectively position $j\equiv 3\pmod{4}$), counting from left to right, the sum of the…
This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…
We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…
We describe the limit zero distributions of sequences of polynomials with positive coefficients.
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by…
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…
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of $P(x)^k Q(x)$, for some Laurent polynomials $P(x)$ and $Q(x)$ in the variable $x$ with integer coefficients. Denoting such…
We determine all perfect powers that can be written as the sum of at most 10 consecutive squares.
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
We give several families of polynomials which are related by Eulerian summation operators. They satisfy interesting combinatorial properties like being integer-valued at integral points. This involves nearby-symmetries and a recursion for…
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps,…
We consider properties of binomial series $\sum_{n=0}^\infty a_n z^{\underline{n}}$, where $z^{\underline{n}}=z(z-1)\cdots(z-n+1)$ and the convergence of binomial series in the complex domain. The order of growth of entire and meromorphic…
We define a class of rational numbers including, as a particular case, the classical harmonic numbers. For one particular instance we apply it to the expansion into powers series of a special function, and also detail its relashionship with…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
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…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…