Related papers: An alternative to Vaughan's identity
Digital identity seems like a prerequisite for digital democracy: how can we ensure "one person, one vote" online without identifying voters? But digital identity solutions - ID checking, biometrics, self-sovereign identity, and trust…
We present two proofs each, all shorter than the original proofs, of two elegant combinatorial identities that came up in the beautiful article arXiv:2010.00077 .
We provide a generalization of the Littlewood identity, both sides of which are related to alternating sign matrices. The classical Littlewood identity establishes a nice product formula for the sum of all Schur polynomials. Compared to the…
Digital avatars are an important part of identity representation, but there is little work on understanding how to represent disability. We interviewed 18 people with disabilities and related identities about their experiences and…
Previously, we proved an identity for theta functions of degree eight, and several applications of it were also discussed. This identity is a natural extension of the addition formula for the Weierstrass sigma-function. In this paper we…
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…
We give a simple formula for some determinants, and an analogous formula for pfaffians, both of which are polynomial identities. The second involve some expressions that interpolate between determinants and pfaffians. We give several…
We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…
In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant.…
Binomial versions of the Andrews-Gordon-Bressoud identities are given.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a…
We combinatorially prove Tetranacci, Tetranacci-Fibonacci, and additional identities using only squares and dominoes on a hexagonal double-strip. Some of these are new proofs of old identities, and others we believe have never been seen…
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
Cutting out and object and estimate its transparency mask is a key task in many applications. We take on the work on closed-form matting by Levin et al., that is used at the core of many matting techniques, and propose an alternative…
As more and more personal photos are shared and tagged in social media, avoiding privacy risks such as unintended recognition becomes increasingly challenging. We propose a new hybrid approach to obfuscate identities in photos by head…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
In this note, we prove some combinatorial identities and obtain a simple form of the eigenvalues of $q$-Kneser graphs.
A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which has as special cases two known identities. Another identity…
Let $E \subseteq \mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the…