This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We giv...

The concept of self-similarity is central to the notion of a fractal, but the actual symmetry group that generates that self-similarity is rarely named, and it seems fractals are almost never studied according to their symmetries. Yet, in other branches of mathematics and physics, it is well understood that symmetry provides a powerful mechanism for understanding systems. In this paper, we iden...

Cancellations are known to be helpful in e cient algebraic computation of polynomials over elds. We de ne a notion of cancellation in Boolean circuits and de ne Boolean circuits that do not use cancellation to be non-cancellative. Non-cancellative Boolean circuits are a natural generalization of monotone Boolean circuits. We show that in the absence of cancellation, Boolean circuits require sup...

We give a definition of the notion spherical varieties in world complex supervarieties with actions algebraic supergroups. A characterization affine is given which generalizes classical case. also explain some general properties monoid highest weights. Several examples are discussed that interesting their own right and highlight differences case, including regular representation, symmetric supe...

Let S be a reduced commutative cancellative atomic monoid. If s is a nonzero element of S, then we explore problems related to the computation of η(s), which represents the number of distinct irreducible factorizations of s ∈ S. In particular, if S is a saturated submonoid of Nd , then we provide an algorithm for computing the positive integer r(s) for which 0 < lim n→∞ η(sn) nr(s)−1 <∞. We fur...

Every cancellative Kleene semigroup satisfies Eilenberg's theorem. Résumé. — Si S est un semigroupe simplifiable de type Kleene, alors S satisfait le théorème d'Eilenberg.

For any finite Coxeter group W , we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W . The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H0(W ), that is, for the symmetric group, the algebra (o...