Related papers: A congruence identity satisfied by m-permutable va…

We introduce superequivalence and superuniform spaces.

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…

We introduce and investigate a series of matching problems for patterns with variables under Simon's congruence. Our results provide a thorough picture of these problems' computational complexity.

A. Mitschke showed that a variety with an $m$-ary near-unanimity term has J\'onsson terms $t_0, \dots, t _{2m-4} $ witnessing congruence distributivity. We show that Mitschke's result is sharp. We also evaluate the best possible number of…

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…

In their recent book on combinatorial identities, Quaintance and Gould devoted one chapter to Melzak's identity. We give new proofs for this identity and its generalization.

A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds…

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.

By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…

In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.

We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then…

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.

In this note, we find a new way to prove several properties of 2-alternating capacities.

In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…

A vector variational principle is proved.

In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.

Based on the work of A. Vershik, we introduce two new combinatorial identities. We show how these identities can be used to prove a new hook-content identity. The main motivation for deriving this identity was a particular optimization…