Related papers: An alternative to Vaughan's identity

In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which…

We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.

Evolutionary games provide the theoretical backbone for many aspects of our social life: from cooperation to crime, from climate inaction to imperfect vaccination and epidemic spreading, from antibiotics overuse to biodiversity…

Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.

In this paper we give new identities involving q-Euler polynomials of higher order.

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…

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…

An elementary proof of an identity by Lyons, Paule and Riese is given. It is simpler than all the 3 published proofs.

On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…

We show that the crossing number of any link that is known to be quasi-alternating is less than or equal to its determinant. Based on this, we conjecture that the crossing number of any quasi-alternating link is less than or equal to its…

We give a short proof of the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity {\em not} involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a…

Face verification systems aim to validate the claimed identity using feature vectors and distance metrics. However, no attempt has been made to bypass such a system using generated images that are constrained by the same feature vectors. In…

We show that the types of the witnesses in the Herbrand functional interpretation can be simplified, avoiding the use of "sets of functionals" in the interpretation of implication and universal quantification. This is done by presenting an…

It is shown that plactic monoids satisfy nontrivial identities.

We present a simple proof and a generalization of a Menon-type identity by Li, Hu and Kim, involving Dirichlet characters and additive characters.

In the conference paper we construct analouge to Pascal's triangle that characterize primes with additional fascinating properties.

A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.

We obtain simple proofs of certain inequalites for bivariate means.

In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach…

By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…