Related papers: The method of creative microscoping
The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for combinatorial designs, and some generalizations, was…
The article addresses the problem whether indefinite double sums involving a generic sequence can be simplified in terms of indefinite single sums. Depending on the structure of the double sum, the proposed summation machinery may provide…
The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further,…
We introduce a new method for building higher-degree sum-of-squares lower bounds over the hypercube $\mathbf{x} \in \{\pm 1\}^N$ from a given degree 2 lower bound. Our method constructs pseudoexpectations that are positive semidefinite by…
We describe a syntactic method for taking proofs which use ultraproducts and translating them into direct, constructive proofs.
In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
We establish two binomial coefficient--generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of…
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of $p$-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We…
We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…
Microstructures, characterized by intricate structures at the microscopic scale, hold the promise of important disruptions in the field of mechanical engineering due to the superior mechanical properties they offer. One fundamental…
The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…
We consider the following problem: Given a nested sum expression, find a sum representation such that the nested depth is minimal. We obtain a symbolic summation framework that solves this problem for sums defined, e.g., over…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
Continuing a series of articles in the past few years on creative telescoping using reductions, we develop a new algorithm to construct minimal telescopers for algebraic functions. This algorithm is based on Trager's Hermite reduction and…
In this chapter tools and techniques from the mathematical theory of formal concept analysis are applied to hypertext systems in general, and the World Wide Web in particular. Various processes for the conceptual structuring of hypertext…
The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of $\C^m$ into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions.…
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…