A Multiset Version of Even-Odd Permutations Identity

In this paper, we present a multiset analogue of the even-odd permutations identity in the context of combinatorics of words. The multiset version is indeed equivalent to the coin arrangements lemma which is a key lemma in Sherman’s proof of Feynman’s conjecture about combinatorial solution of Ising model in statistical physics. Here, we give a bijective proof which is based on the standard factorization of a Lyndon word.

Decidable Inequalities over Infinite Trees

Linear tree constraints are given by pointwise linear inequalities between infinite trees labeled with nonnegative rational numbers. Satisfiablity of such constraints is at least as hard as solving the Skolem-Mahler-Lech Problem. We provide an interesting subcase, for which we prove that satisfiablity is decidable. Our decision procedure is based on intricate arguments using automata and combinatorics of words.Our subcase allows to construct an inference mechanism for resource bounds of object oriented Java-like programs: actual resource bounds can be read off from solutions of tree constraints. So far, only the case of degenerated tree constraints (i.e. lists) was known to be decidable which, however, is insufficient to generally solve the given resource analysis problem. The present paper therefore provides a generalisation to trees of higher degree in order to cover the entire range of constraints encountered by resource analysis.

Les associations de marqueurs discursifs – De la cooccurrence libre à la collocation

The question of the syntagmatic combinatorics of words belonging to the classes commonly addressed by grammatical tradition (such as nouns, verbs, adjectives and adverbs) has been a subject of sustained reflection for several decades. The situation is different for discourse markers (DMs), which have gained substantial interest only recently (toward the end of the 1990s). This article takes as its starting point the idea that DMs are subject to the same types of syntagmatic associations as words belonging to the "ordinary" classes. By analogy with these classes, three types of syntagmatic associations are distinguished in the domain of DMs: the free discursive co-occurrence, the fixed expression (or discursive locution), and the semi-fixed expression (or discursive collocation). Of these types of word associations, the semi-fixed expression proves the most original and the most delicate to examine. It is therefore spe-cifically analyzed in this text, namely through a study of one marker in particular: don ([dɔ̃]).

Some considerations on Hydra groups and a new bound for the length of words

After a survey on some recent results of Riley and others on Ackermann functions and Hydra groups, we make an analogy between DNA sequences, whose growth is the same of that of Hydra groups, and a musical piece, written with the same algorithmic criterion. This is mainly an aesthetic observation, which emphasizes the importance of the combinatorics of words in two different contexts. A result of specific mathematical interest is placed at the end, where we sharpen some previous bounds on deterministic finite automata in which there are languages with hairpins.

Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras

We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. Like all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the considered problem and combinatorics of words.