A function on an algebra is congruence preserving if, for any congruence, it maps congruent elements to congruent elements. We show that, on a free monoid generated by at least three letters, a function from the free monoid into itself is congruence preserving if and only if it is of the form x 7→ w0xw1 · · ·wn−1xwn for some finite sequence of words w0, . . . , wn. We generalize this result to ...

We study formulas for Fibonacci numbers as sums over compositions. The Fibonacci number Fn+1 is the number of compositions of n with parts 1 and 2. Compositions with parts 1 and 2 form a free monoid under concatenation, and our formulas arise from free submonoids of this free monoid.

Cet article pr esente une etude combinatoire du mono de Chinois, un mono de ternaire proche du mono de plaxique, fond e sur le sch ema cba bca cab. Un algo-rithme proche de l'algorithme de Schensted nous permet de caract eriser les classes d' equivalence et d'exhiber une section du mono de. Nous enonn cons egalement une correspondance de Robinson-Schensted pour le mono de Chinois avant de nous ...

We study properties of the forgotten monoid which appeared in work of Lascoux and Schützenberger and recently resurfaced in the construction of dual equivalence graphs by Assaf. In particular, we provide an explicit characterization of the forgotten classes in terms of inversion numbers and show that there are n − 3n + 4 forgotten classes in the symmetric group Sn. Each forgotten class contains...

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