Related papers: Combinatorial inequalities
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
In this short note, we improve the famous Reid Inequality related to linear operators.
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
In this paper we replay the definitions, constructions and results from [SIAM J. Sci. Comp., 37(3)(2015), A1248-A1269] by completing and developing some of them to inconsistent least squares problems.
Work in progress concerning alternative formalizations of arithmetic.
We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].
This is the rejoinder for discussion of "Multinomial Inverse Regression for Text Analysis", Journal of the American Statistical Association 108, 2013.
This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in n-dimensions. Moreover, we discuss how the latter are related to the monotonicity of an…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
This paper is a companion to our prior paper arXiv:0705.4619 on the `Small Ball Inequality in All Dimensions.' In it, we address a more restrictive inequality, and obtain a non-trivial, explicit bound, using a single essential estimate from…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown,…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…