The order of hypersubstitutions, all idempotent elements on the monoid of all hypersubstitutions of type τ 2 were studied by K. Denecke and Sh. L. Wismath and all idempotent elements on the monoid of all hypersubstitutions of type τ 2, 2 were studied by Th. Changpas and K. Denecke. We want to study similar problems for the monoid of all generalized hypersubstitutions of type τ 2 . In this paper...

We consider a common generalization of the embedding and intersection problems for latin squares. Specifically, we extend the definition of embedding to squares whose sides do not meet the necessary condition for embedding and extend the intersection problem to squares of different orders. Results are given for arbitrary latin squares, and those which are idempotent and idempotent symmetric. Th...

A language L ⊆ A∗ is literally idempotent in case that uav ∈ L if and only if uav ∈ L, for each u, v ∈ A∗, a ∈ A. We already studied classes of such languages closely related to the (positive) varieties of the famous StraubingThérien hierarchy. In the present paper we start a systematic study of literal varieties of literally idempotent languages, namely we deal with the case of two letter alph...

The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960’s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green’s relation J is tri...

We show that every (finite or not) typing derivation of system M, using non-idempotent intersection, which is the infinitary version of de Carvalho’s system M0, can be represented in a rigid, non-idempotent intersection type system S. Namely, whereas non-idempotent intersection is represented by multisets in system M, system S resort to families of types indexed by integers, called tracks. The ...

We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms whi...

Cyclic codes are very useful in error correcting codes. Hence, the construction of good cyclic codes is of utmost importance. A generic class of polynomials called generator polynomials is used to construct the cyclic codes. Finding a generator polynomial necessitates factoring a base polynomial called monic polynomial. Unfortunately, factoring a polynomial is not always an easy task. Idempoten...

A graph G is said to be hom-idempotent if there is a homomorphism from G2 to G, and weakly hom-idempotent if for some n ≥ 1 there is a homomorphism from Gn+1 to Gn . We characterize both classes of graphs in terms of a special class of Cayley graphs called normal Cayley graphs. This allows us to construct, for any integer n, a Cayley graph G such that Gn+1 → Gn 6→ Gn−1, answering a question of ...

When distributed clients query or update shared data, eventual consistency can provide better availability than strong consistency models. However, programming and implementing such systems can be difficult unless we establish a reasonable consistency model, i.e. some minimal guarantees that programmers can understand and systems can provide effectively. To this end, we propose a novel consiste...