Related papers: A congruence identity satisfied by m-permutable va…
It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a…
We completely determine all varieties of monoids on whose free objects all fully invariant congruences or all fully invariant congruences contained in the least semilattice congruence permute. Along the way, we find several new monoid…
In this paper we present many congruences for several Ap\'ery-like sequences.
We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.
In investigating the properties of a certain class of homogeneous polynomials, we discovered an identity satisfied by their coefficients which involves simple 2F1 Gauss hypergeometric functions. This result appears to be new and we supply a…
It is shown that plactic monoids satisfy nontrivial identities.
A family of general integral identities is derived and several applications of physical interest are presented
We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
We present a new twist on an old identity.
In this note, after recalling a proof of the Macdonald identities for untwisted affine root systems, we derive the Macdonald identities for twisted affine root systems.
It is proved that the five well-known identities universally satisfied by commutators in a group generate all universal commutator identities for commutators of weight 4.
The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic…
The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised $_6\phi_5$ series.
We give a combinatorial proof that congruence permutability is prime in the lattice of interpretability types of varieties. Thereby, we settle a 1984 conjecture of Garcia and Taylor.
We prove a master identity for a class of sequences defined by full-history linear homogeneous recurrences with (non-negative) constant coefficients. The identity is derived in a combinatorial way, providing thus combinatorial proofs for…
We develop the basic properties of the higher commutator for congruence modular varieties.
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…