Related papers: A Million-dollar Proof
Let $n$ be an odd positive integer. In this short elementary note, we slightly extend Macdonald's identity for $\mathfrak{sl}_{n}$ into a two-variables identity in the spirit of Jacobi forms. The peculiarity of this work lies in its proof…
We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.
We show that, up to multiplication by a factor $\frac{1}{(cq;q)_{\infty}}$, the weighted words version of Capparelli's identity is a particular case of the weighted words version of Primc's identity. We prove this first using recurrences,…
Person re-identification (re-id) is a pivotal task within an intelligent surveillance pipeline and there exist numerous re-id frameworks that achieve satisfactory performance in challenging benchmarks. However, these systems struggle to…
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.
In this article, a short combinatorial proof of the Capelli's identity is given. It also leads to an easy proof of the Capelli--Cauchy--Binet identity, a more general form of Capelli's identity. With the technique introduced, the Turnbull's…
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
This work addresses the task of long-term person re-identification. Typically, person re-identification assumes that people do not change their clothes, which limits its applications to short-term scenarios. To overcome this limitation, we…
What if you could really revoke your actual biometric identity, and install a new one, by live rewriting your biological self? We propose some novel mechanisms for hot swapping identity based in novel biotechnology. We discuss the potential…
The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive $m$-versions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised…
The object of this paper is to propose and prove a new generalization of the Andrews-Gordon identities, extending a recent result of Garrett, Ismail and Stanton. We also give a combinatorial discussion of the finite form of their result,…
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
This paper presents a new identity based strong designated verifier parallel multi-proxy signature scheme. Multi-Proxy signatures allow the original signer to delegate his signing power to a group of proxy signers. In our scheme, the…
A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of…
In 2018, Stanton proved two types of generalisations of the celebrated Andrews--Gordon and Bressoud identities (in their $q$-series version): one with a similar shape to the original identities, and one involving binomial coefficients. In…
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
In this article we prove some identities which allow us to evaluate some multiple unit square integrals. In our examples we will give the value of some double and triple integrals. Then, we prove several classical integral formulas with the…
We investigate identity lease, a new type of service in which users lease their identities to third parties by providing them with full or restricted access to their online accounts or credentials. We discuss how identity lease could be…
Existing claim verification datasets often do not require systems to perform complex reasoning or effectively interpret multimodal evidence. To address this, we introduce a new task: multi-hop multimodal claim verification. This task…
We report on findings of a variant of ${\texttt{IdentityFinder}}$ - a Maple program that was used by two of the authors to conjecture several new identities of Rogers-Ramanujan kind. In the present search, we modify the parametrization of…