Related papers: Combinatorial inequalities
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…
Certain new inequalities for the sums of factorials are presented.
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…
We translate inequalities and conjectures for immanants and generalized matrix functions into inequalities in the L\"owner order. These have the form of trace polynomials and generalize the inequalities from [FH, J. Math. Phys. 62 (2021),…
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
This is a companion overview paper to arXiv:2409.17489: we give all the main definitions, constructions and statements, but no proofs.
We obtain simple proofs of certain inequalites for bivariate means.
Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
This is the article by the same name which was published in the March 2016 issue of the AMS Notices. Due to space constraints, some references contained here were not provided in the published version were not provided. The figures in this…
This is an extended version of our note in the Notices of the American Mathematical Society 63 (2016), no. 9, in which we explain what multiple orthogonal polynomials are and where they appear in various applications.
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final…
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…
This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…
Ruzsa's equivalence theorem provided a framework for converting certain families of inequalities in additive combinatorics to entropic inequalities (which sometimes did not possess stand-alone entropic proofs). In this work, we first…