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On the construction of permutations of a given type kept fixed by conjugation

✍ Scribed by Ivan Constantineau; Jacques Labelle

Book ID
107885198
Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
387 KB
Volume
62
Category
Article
ISSN
0097-3165

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Let \_ # S k and { # S n be permutations. We say { contains \_ if there exist Stanley and Wilf conjectured that for any \_ # S k there exists a constant c=c(\_) such that F(n, \_) c n for all n. Here we prove the following weaker statement: For every fixed \_ # S k , F(n, \_) c n#\* (n) , where c=c

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Let S be a finite set and u a permutation on S. The permutation u\* on the set of 2-subsets of S is naturally induced by u. Suppose G is a graph and V(G), €(G) are the vertex set, the edge set, respectively. Let V(G) = S. If €(G) and u\*(€(G)), the image of €(G) by u\*, have no common element, then