Related papers: An alternative to Vaughan's identity
Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other…
Human face as a physical human recognition can be used as a unique identity for computer to recognize human by transforming human face with face algorithm as simple text number which can be primary key for human. Human face as single…
We show that Naming-- the existence of distinct IDs known to all-- is a hidden but necessary assumption of Herlihy's universality result for Consensus. We then show in a very precise sense that Naming is harder than Consensus and bring to…
We prove a generalization of the Capelli identity. As an application we obtain an isomorphism of the Bethe subalgebras actions under the (gl(N),gl(M)) duality.
We derive two new identities involving the Bernoulli numbers, the Euler numbers, and the Stirling numbers of the first kind using analytic continuation of a well known identity for the Stirling numbers of the first kind.
While there are many identities involving the Euler and Bernoulli numbers, they are usually proved analytically or inductively. We prove two identities involving Euler and Bernoulli numbers with combinatorial reasoning via up-down…
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
We prove that a curious generating series identity implies Faber's intersection number conjecture (by showing that it implies a combinatorial identity already given in arXiv:1902.02742) and give a new proof of Faber's conjecture by directly…
We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.
An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.
We produce a new, shorter construction of a minor-universal planar graph.
Foster's network theorems and their extensions to higher orders involve resistance values and conductances. We establish identities concerning voltage values and conductances. Our identities are analogous to the extended Foster's…
Scientists have traditionally limited the mechanisms of social cognition to one brain, but recent approaches claim that interaction also realizes cognitive work. Experiments under constrained virtual settings revealed that interaction…
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.
In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.
This paper describes a new model which generates images in novel poses e.g. by altering face expression and orientation, from just a few instances of a human subject. Unlike previous approaches which require large datasets of a specific…
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
We give several applications of an identity for sums of weakly stationary sequences due to Ky Fan.
In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.
We address the problem of person re-identification (reID), that is, retrieving person images from a large dataset, given a query image of the person of interest. A key challenge is to learn person representations robust to intra-class…