Related papers: A Million-dollar Proof
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
We give combinatorial proofs for some identities involving binomial sums that have no closed form.
We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.
We show a new proof for the load of obtained by a Cuckoo Hashing data structure. Our proof is arguably simpler than previous proofs and allows for new generalizations. The proof first appeared in Pinkas et. al. \cite{PSWW19} in the context…
Given a set of financial transactions (who buys from whom, when, and for how much), as well as prior information from buyers and sellers, how can we find fraudulent transactions? If we have labels for some transactions for known types of…
In this short note we provide some algebraic identity with a proof exploiting its probabilistic interpretation. We show several consequences of the identity, in particular we obtain a new representation of a Stirling number of second kind,…
A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.
In this note, we find a new way to prove several properties of 2-alternating capacities.
We give new proofs of MacMahon and Russell's modulo 6 identities using the method of weighted words. We also present a new refinement of MacMahon's identity, some related finite sum identities, and a companion partition theorem to sequence…
A variation on the splitting principle
We present a new, elementary, dynamical proof of the prime number theorem.
A family of general integral identities is derived and several applications of physical interest are presented
We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating…
We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.
Not all people are equally easy to identify: color statistics might be enough for some cases while others might require careful reasoning about high- and low-level details. However, prevailing person re-identification(re-ID) methods use…
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
We show that a binomial identity arising in the context of the study of series expansions of $1/\pi$ can be seen as an incarnation of Whipples second theorem for hypergeometric series.
This paper presents a new family of almost identities. These are based on series that sum to elements close to either rationals or rational multiples of pi. The explanation of the phenomenon takes its roots in the theory of Mellin…
We give "hybrid" proofs of the $q$-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the…
We present a new proof for the main claim made in the author's paper "On the identity bases of Brandt semigroups" (Ural. Gos. Univ. Mat. Zap. 14, no.1 (1985), 38--42); this claim provides an identity basis for an arbitrary Brandt semigroup…