A characterization of one-element commutation classes
 
 
Description: 

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 talk we present 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. 

Date:  2024-03-13
Start Time:   16:00
Speaker:  Diogo Soares (CMUC, UC|UP PhD student)
Institution:  CMUC - Universidade de Coimbra
Place:  Sala 2.4, DMUC
Research Groups: -Algebra and Combinatorics
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