The polynomial of a permutation representation
نویسندگان
چکیده
منابع مشابه
The Polynomial of a Permutation Representation*
Let (G, D) be a permutation representation of a finite group G acting on a finite set D. The cycle index of this representation is a polynomial P(G, D; Xl ,..., x,~) in several variables xl ,..., x~ with rational numbers as coefficients (see [1]). The restriction, made in [1], that the representation (G, D) is faithful, is unnecessary and we put no restriction on (G, D) whatsoever. We replace e...
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The cycle polynomial of a finite permutation group G is the generating function for the number of elements of G with a given number of cycles:
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Permutation Classes of Polynomial Growth
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterized as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue all ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1968
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(68)80045-6