Graphs of Reduced Words and Some Connections
Abstract
The family of graphs of reduced words of a certain subcollection of permutations in the union n≥ 4Sn 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.
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