منابع مشابه
Enumerating projective reflection groups
Projective reflection groups have been recently defined by the second author. They include a special class of groups denoted G(r, p, s, n) which contains all classical Weyl groups and more generally all the complex reflection groups of type G(r, p, n). In this paper we define some statistics analogous to descent number and major index over the projective reflection groups G(r, p, s, n), and we ...
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We prove that the set of limit groups is recursively enumerable, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (à la Long and Reid) is coherent and, furthermore, there exists an algorithm that computes presentations for finitely generated subgroups. The other main ingredient is the ability to algorithmicall...
متن کاملEnumerating Palindromes in Rank Two Free Groups
Conjugacy classes of primitive words in the free group of rank two can indexed by the rationals. A representative for each conjugacy class is given by a recursive enumeration scheme and the representative, usually called a Farey word, is denoted by Wp/q where p and q are relatively prime integers. Primitive pairs, that is, pairs of words that generate the free group, correspond to pairs of word...
متن کاملEnumerating Palindromes and Primitives in Rank Two Free Groups
Let F = 〈a, b〉 be a rank two free group. A word W (a, b) in F is primitive if it, along with another group element, generates the group. It is a palindrome (with respect to a and b) if it reads the same forwards and backwards. It is known that in a rank two free group any primitive element is conjugate either to a palindrome or to the product of two palindromes, but known iteration schemes for ...
متن کاملEnumerating Excedances with Linear Characters in Classical Weyl Groups
Several signed excedance-type statistics have nice formulae when summed over the symmetric group and over the hyperoctahedral group. Motivated by these, we consider sums of the form fχ,n(q) = ∑ w∈W χ(w)q exc(w) where W is a classical Weyl group of rank n, χ is a non-trivial one-dimensional character of W , and exc(w) is the excedance statistic of w. We give formulae for these sums in a more gen...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1999
ISSN: 0263-6115
DOI: 10.1017/s1446788700001166