Related papers: Combinatorial inequalities
This article gives a brief survey of the theory and applications of anomalies.
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
We present a new corpus comprising annotations of medical entities in case reports, originating from PubMed Central's open access library. In the case reports, we annotate cases, conditions, findings, factors and negation modifiers.…
This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…
This note addresses the input and output of intervals in the sense of interval arithmetic and interval constraints. The most obvious, and so far most widely used notation, for intervals has drawbacks that we remedy with a new notation that…
This is supplementary material to "Realizations of a special class of admittances with strictly lower complexity than canonical forms" [1], which presents the detailed proofs of some results. For more background information, refer to…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
We obtain new inequalities with alternating signs of H\"{o}lder and Minkowski type.
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…
The content of this paper is now available as part of arXiv:0802.2019
We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
By polynomial (or extended binomial) coefficients, we mean the coefficients in the expansion of integral powers, positive and negative, of the polynomial $1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish several…
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Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds…
We give a summary of recent progress on the signed area enumeration of closed walks on planar lattices. Several connections are made with quantum mechanics and statistical mechanics. Explicit combinatorial formulae are proposed which rely…