Permutations and Combinations of Colored Multisets
Department of Mathematics
West Virginia University
Morgantown, WV 26506
Department of Mathematical Sciences
State University of New York at Fredonia
Fredonia, NY 14063
Given positive integers
, each with a distinct color. This paper discusses two types of
combinatorial identities associated with the permutations and
. The first identity provides, for
-fold sum for
. The second type of
identities can be expressed in terms of the Hermite polynomial, and
counts color-symmetrical permutations of
, which are
permutations whose underlying uncolored permutations remain fixed
after reflection and a permutation of the uncolored numbers.
Full version: pdf,
(Concerned with sequence
Received June 22 2009; revised versions received July 3 2009; November
9 2009; December 21 2009; February 18 2010.
Published in Journal of Integer Sequences, February 18 2010.
Journal of Integer Sequences home page