Rapid calculation of shuffles of two words
Theoretical Computer Science
Combinatorics on traces
Automata, Languages, and Machines
Automata, Languages, and Machines
Shuffle factorization is unique
Theoretical Computer Science
Shuffle of omega-Words: Algebraic Aspects (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Two optimal parallel algorithms on the commutation class of a word
Theoretical Computer Science - Words, languages and combinatorics
On a conjecture of schnoebelen
DLT'03 Proceedings of the 7th international conference on Developments in language theory
On the minimal automaton of the shuffle of words and araucarias
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Erratum for "Shuffle of Words and Araucaria Trees"
Fundamenta Informaticae
Araucaria Trees: Construction and Grafting Theorems
Fundamenta Informaticae
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The shuffle of k words $u_1$,…,$u_k$ 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 k0.