2024/06/14 by Adeyemo, Praise
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2406.09666
The family of graphs of reduced words of a certain subcollection of permutations in the union ∪n≥ 4\frakSn of symmetic groups is investigated. The subcollection is characterised by the hook cycle type (n-2,1,1) with consecutive fixed points. A closed formula for counting the vertices of each member of the family is given and the vertex-degree polynomials for the graphs with their generating series is realised. Lastly, some isomorphisms of these graphs with various combinatorial objects are established.