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Full-Text Articles in Applied Mathematics
The Proportion Of Fixed-Point-Free Elements Of A Transitive Permutation Group, Nigel Boston, Walter Dabrowski, Tuval Foguel, Paul J. Gies, Judy Leavitt Walker, David T. Ose, David A. Jackson
The Proportion Of Fixed-Point-Free Elements Of A Transitive Permutation Group, Nigel Boston, Walter Dabrowski, Tuval Foguel, Paul J. Gies, Judy Leavitt Walker, David T. Ose, David A. Jackson
Department of Mathematics: Faculty Publications
In 1990 Hendrik W. Lenstra, Jr. asked the following question: if G is a transitive permutation group of degree n and A is the set of elements of G that move every letter, then can one find a lower bound (in terms of n) for f(G) = |A|/|G|? Shortly thereafter, Arjeh Cohen showed that 1/n is such a bound.
Lenstra’s problem arose from his work on the number field sieve. A simple example of how f(G) arises in number theory is the following: if h is an irreducible polynomial …