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Erratum for "Shuffle of Words and Araucaria Trees"

Schott R., Spehner J-C.

Fundamenta Informaticae

2007

Vol. 81, nr 4

485-490

The starting definitions of araucarias given in [1] contain some mistakes. We give here new definitions which replace Definitions 2.2, 2.3 and 2.4, Theorem 2.1 and Corollary 2.1. The rest of the paper is based on the characterization of araucarias given in Theorem 1.1 and remains true with these corrections.

Shuffle of Words and Araucaria Trees

Schott R., Spehner J-C.

Fundamenta Informaticae

2006

Vol. 74, nr 4

579-601

The shuffle of k words u1,..., uk is the set of words obtained by interleaving the letters of these words such that the order of appearance of all letters of each word is respected. The study of the shuffle product of words leads to the construction of an automaton whose structure is deeply connected to a family of trees which we call araucarias. We prove many structural properties of this family of trees and give some combinatorial results. We introduce a family of remarkable symmetrical polynomials which play a crucial role in the computation of the size of the araucarias. We prove that the minimal partial automaton which recognizes the shuffle of a finite number of special words contains an araucaria for each integer k > 0.