Related papers: Additive double character sums over some structure…
We present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
By the additive property, we mean a condition under which $L^p$ spaces over finitely additive measures are complete. Basile and Rao gives a necessary and sufficient condition that a finite sum of finitely additive measures has the additive…
This paper establishes new upper bounds for the sum of the $k$ largest eigenvalues of symmetric matrices. When applied to the adjacency matrix of a graph, our results improve upon a related bound due to Mohar {\bf [On the sum of k largest…
Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…
A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
This note is a continuation of an earlier paper by the authors. We describe improved constructions addressing a question of Erd\H{o}s and Szemer\'edi on sums and products of real numbers along the edges of a graph. We also add a few…
Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological string theories (CTST). These CTST were based on…
We classify the polynomials $f(x,y) \in \mathbb R[x,y]$ such that given any finite set $A \subset \mathbb R$ if $|A+A|$ is small, then $|f(A,A)|$ is large. In particular, the following bound holds : $|A+A||f(A,A)| \gtrsim |A|^{5/2}.$ The…
In this paper we introduce a graph structure, called subspace sum graph $\mathcal{G}(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ where the vertex set is the collection of non-trivial proper subspaces of a vector space and…
We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.
We improve upon the upper bounds for the cardinality of the value set of a multivariable polynomial map over a finite field using the polytope of the polynomial. This generalizes earlier bounds only dependent on the degree of a polynomial.
Chowla~(1962), McEliece~(1974), Evans~(1977, 1981) and Aoki~(1997, 2004, 2012) studied Gauss sums, some integral powers of which are in the field of rational numbers. Such Gauss sums are called {\it pure}. In particular, Aoki (2004) gave a…
Permutation polynomials over finite fields have taken an important role in vast areas in mathematics as well as engineering. Recently, Tu et al. gave some classes of complete permutation polynomials over finite fields of even…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
We give an upper bound on the number of perfect matchings in simple graphs with a given number of vertices and edges. We apply this result to give an upper bound on the number of 2-factors in a directed complete bipartite balanced graph on…
The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of…