Related papers: A Million-dollar Proof
A close look at double-quantified statements in a playful setting.
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
In this paper, we present a method to automatically compare multiple radiographs in order to find the identity of a patient out of the dental features. The method is based on the matching of image features, previously extracted by computer…
In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new…
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 discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
In this paper we present our variant of quantum antisymmetry and quantum Jacobi identity.
In a recent paper, Caracciolo, Sokal and Sportiello presented, inter alia, an algebraic/combinatorial proof for Cayley's identity. The purpose of the present paper is to give a "purely combinatorial" proof for this identity; i.e., a proof…
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…
We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve…
In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.
A number of identities are proved by using Stirling transforms. These identities involve Stirling numbers of the first and second kinds, hyperharmonic and derangement numbers, Bernoulli and Euler numbers and polynomials, powers, power sums,…
A probability method is provided to prove three classes of combinatorial identities. The method is extremely simple, only one step after the proper probability setup.
We motivate and develop a new line of digital forensics. In the meanwhile, we propose a novel approach to photographer identification, a rarely explored authorship attribution problem. We report a proof-of-concept study, which shows the…
We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.
We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a different proof of an identity in another article by…
Consider a mechanism that cannot observe how many players there are directly, but instead must rely on their self-reports to know how many are participating. Suppose the players can create new identities to report to the auctioneer at some…
I revisit an automated proof of Andrews' pentagonal number theorem found by Riese. I uncover a simple polynomial identity hidden behind his proof. I explain how to use this identity to prove Andrews' result along with a variety of new…