The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M . For string compression, straight-line programs, i.e., contextfree grammars that generate a single string, are used in this paper. It is shown that the compressed word problem for a free inverse monoid of finite rank at least two is comp...

This paper generalizes the notion of a toric variety. In particular, these generalized toric varieties include examples of non-normal non-quasiprojective toric varieties. Such an example seems not to have been noted before in the literature. This generalization is achieved by replacing a fan of strictly rational polyhedral cones in a lattice with a monoided space, that is a topological space eq...

Based Based on on two two inversion inversion formulas formulas for for enumerating enumerating words words in in the the free free monoid monoid by by adjacencies, adjacencies, we we present present a a new new approach approach to to a a class class of of permutation permutation problems problems having having Eulerian-type Eulerian-type generating generating functions. functions. We We also ...

Given a ∨ -complete (semi)lattice L, we consider L-labeled transition systems as coalgebras of a functor L(−), associating with a set X the set LX of all L-fuzzy subsets. We describe simulations and bisimulations of L-coalgebras to show that L(−) weakly preserves nonempty kernel pairs iff it weakly preserves nonempty pullbacks iff L is join infinitely distributive (JID). Exchanging L for a comm...

Article history: Received 3 February 2013 Accepted 7 August 2013 Communicated by M. Ito

Cet article pr esente une etude combinatoire du mono de hypoplaxique. Apr es avoir rappel e les d eenitions classiques, nous exhibons un algorithme qui est l'analogue hypoplaxique de l'algorithme de Schensted puis nous donnons un certain nombre de propri et es int eressantes de ce mono de. Abstract This paper presents a combinatorial study of the hypoplactic monoid. After having recalled the ba...

It is established here that it is decidable whether a rational set of a free partially commutative monoid (i.e. trace monoid) is recognizable or not if and only if the commutation relation is transitive (i.e. if the trace monoid is isomorphic to a free product of free commutative monoids). The bulk of the paper consists in a characterization of recognizable sets of free products via generalized...

We prove that if M is a monoid and A a finite set with more than one element, then the residual finiteness of M is equivalent to that of the monoid consisting of all cellular automata over M with alphabet A.