Geodesic
A characterization of one-element commutation classes
Ricardo Mamede1 ; José Luis Santos1 ; Diogo Soares1
1Universidade de Coimbra
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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A reduced word for a permutation of the symmetric group is its own commutation class if it has no commutation moves available. These words have the property that every factor of length 2 is formed by consecutive integers, but in general words of this form may not be reduced. In this paper we give a necessary and sufficient condition for a word with the previous property to be reduced. In the case of involutions, we give an explicitly construction of their one-element commutation classes and relate their existence with pattern avoidance problems.
DOI : 10.37236/12744
Classification : 05A05, 20F55
Mots-clés : one-element commutation classes, pattern avoidance problems

Ricardo Mamede  1   ; José Luis Santos  1   ; Diogo Soares  1

1 Universidade de Coimbra 
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Ricardo Mamede; José Luis Santos; Diogo  Soares. A characterization of one-element commutation classes. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12744

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