7 research outputs found
On Graphs of Sets of Reduced Words
Any permutation in the finite symmetric group can be written as a product of
simple transpositions . For a fixed permutation the products of minimal length are called reduced
decompositions or reduced words, and the collection of all such reduced words
is denoted . Any reduced word of can be
transformed into any other by a sequence of commutation moves or long braid
moves. One area of interest in these sets are the congruence classes defined by
using only braid or only commutation relations. The set
can be drawn as a graph, , where the vertices are the reduced words,
and the edges denote the presence of a commutation or braid move between the
words. This paper presents new work on subgraph structures in , as
well as new formulas to count the number of braid edges and commutation edges
in . We also include work on bounds for the number of braid and
commutation classes in .Comment: 24 pages, 10 figure
Enumeration of Standard Young Tableaux
A survey paper, to appear as a chapter in a forthcoming Handbook on
Enumeration.Comment: 65 pages, small correction