Related papers: The Method of Multiple Combinatorial Telescoping

We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews and Gordon involving $q$-trinomial coefficients. We follow…

These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…

We prove a double binomial sum identity which differs from most binomial sum identities in that the summands involve the absolute value function. The identity is of interest because it can be used in proofs of lower bounds for the Hadamard…

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…

An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geometric approach reveals the role played by the symmetries of…

We lay the combinatorial foundations for [ShSt:340] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.

Usually creative telescoping is used to derive recurrences for sums. In this article we show that the non-existence of a creative telescoping solution, and more generally, of a parameterized telescoping solution, proves algebraic…

We present the method of multiplexed imaging designed for astronomical observations of large sky areas in the IR, visible and UV frequencies. Our method relies on the sparse nature of astronomical observations. The method consists of an…

We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.

A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which has as special cases two known identities. Another identity…

We discuss two approaches to producing generalized parity proofs of the Kochen-Specker theorem. Such proofs use contexts of observables whose product is $I$ or $-I$; we call them constraints. In the first approach, one starts with a fixed…

Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.

We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed…

We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a…

Andrews and El Bachraoui recently studied various two-colored integer partitions, including those related to two-colored partitions into distinct parts with constraints and overpartitions. Their work raised questions about the existence of…

By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.

We give a proof of two identities involving binomial sums at infinity conjectured by Z-W Sun. In order to prove these identities, we use a recently presented method i.e. we view the series as specializations of generating series and derive…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of partial and…

We present the statistical approach to the combining of signal significances.