Automata, reduced words and Garside shadows in Coxeter groups
نویسندگان
چکیده
منابع مشابه
Reduced words in affine Coxeter groups
Let r(w) denote the number of reduced words for an element w in a Coxeter group w. Stanley proved a formula for r(w) when W is the symmetric group A,,, and he suggested looking at r(w) for the ffie group Aln. We prove that for any afline Coxeter group R, there is a finite number of types of elements in xX, such that to every element w can be associated (I) a type t, (2) an element u in the &rit...
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Consider a graph with vertex set S. A word in the alphabet S has the intervening neighbours property if any two occurrences of the same letter are separated by all its graph neighbours. For a Coxeter graph, words represent group elements. Speyer recently proved that words with the intervening neighbours property are irreducible if the group is infinite and irreducible. We present a new and shor...
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We analyze the structure of reduced expressions in the Coxeter groups An, Bn and Dn. Several special classes of elements are singled out for their connections with symmetric functions or the theory of P -partitions. Membership in these special classes is characterized in a variety of ways, including forbidden patterns, forbidden subwords, and by the form of canonically chosen reduced words.
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The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common ...
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In the standard Coxeter presentation, the symmetric group Sn is generated by the ad jacent transpositions (1,2), (2,3), ... , (n1,n). For any given permutation, we consider all minimal-length factorizations thereof as a product of the generators. Any two transpositions (i,i+1) and (j,j+1) commute if the numbers i and j are not consecutive; thus, in any factorization, their order can be switche...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.04.006