A Symmetric Function Resolution of the Number of
Permutations With Respect to Block-Stable Elements

D.M. Jackson and M. Yip

Department of Combinatorics and Optimization, University of Waterloo,
200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada

{dmjackson, m2yip}@math.uwaterloo.ca

Annals of Combinatorics 10 (4) p.463-480 December, 2006

Abstract:

We consider a question raised by Suhov and Voice from quantum information theory
and quantum computing. An element of a partition of {1, …, *n*} is said to be block-stable for
if it is not moved to another block under the action of
The problem concerns the determination
of the generating series for elements of with respect to the number of blockstable
elements of a canonical partition of a finite *n*-set, with block sizes *k*_{1}, … *k*_{r}, in terms of
the moment (power) sums *p*_{q}(*k*_{1}, … *k*_{r}). We also consider the limit
*r*)/*r*^{n} subject to the condition that exists for *q*=1,2,….

References:

1. S. Even and J. Gillis, Derangements and Laguerre polynomials, Math. Proc. Cambridge Philos. Soc. 79 (1) (1976) 135-143.

2. I.P. Goulden and D.M. Jackson, Combinatorial Enumeration, Wiley, New York, 1983.

3. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd. Ed., Oxford University Press, New York, 1995.

4. Y. Suhov and T. Voice, Private communication, November 11, 2002.