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- W4226075449 abstract "Any permutation in the finite symmetric group can be written as a product of simple transpositions $s_i = (i~i+1)$. For a fixed permutation $sigma in mathfrak{S}_n$ the products of minimal length are called reduced decompositions or reduced words, and the collection of all such reduced words is denoted $R(sigma)$. Any reduced word of $sigma$ 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 $R(sigma)$ can be drawn as a graph, $G(sigma)$, where the vertices are the reduced words, and the edges denote the presence of a commutation or braid move between the words. This paper will present brand new work on subgraph structures in $G(sigma)$, as well as new formulas to count the number of braid edges and commutation edges in $G(sigma)$. We will also include work on bounds for $|B(sigma)|$ and $|C(sigma)|$." @default.
- W4226075449 created "2022-05-05" @default.
- W4226075449 creator A5032986046 @default.
- W4226075449 date "2022-01-30" @default.
- W4226075449 modified "2023-09-24" @default.
- W4226075449 title "Graphs of Sets of Reduced Words" @default.
- W4226075449 doi "https://doi.org/10.48550/arxiv.2201.12887" @default.
- W4226075449 hasPublicationYear "2022" @default.
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