6 research outputs found
Sign-Balanced Pattern-Avoiding Permutation Classes
A set of permutations is called sign-balanced if the set contains the same
number of even permutations as odd permutations. Let be the set of permutations in the symmetric group
which avoids patterns . The aim of this
paper is to investigate when, for certain patterns , is sign-balanced for
every integer . We prove that for any , if is
sign-balanced except , then is sign-balanced for every integer . In addition, we
give some results in the case of avoiding some patterns of length
Restricted even permutations and Chebyshev polynomials
We study generating functions for the number of even (odd) permutations on n
letters avoiding 132 and an arbitrary permutation on k letters, or
containing exactly once. In several interesting cases the generating
function depends only on k and is expressed via Chebyshev polynomials of the
second kind.Comment: 20 page