The University of Michigan Combinatorics Seminar
Winter 2002
March 29, 4:10-5:00, 4088 East Hall
(pre-talk 3:10-4:40, 4088 East Hall)

Border strips, codes, and snakes of skew partitions

Richard Stanley



A skew partition may be regarded as the Ferrers (or Young) diagram of a partition of an integer n, with a smaller such diagram removed from the upper left corner. A border strip is a skew partition whose diagram is (rookwise) connected and contains no 2 x 2 square. Border strips first arose naturally in the Murnaghan-Nakayama rule, which gives a combinatorial description of the values of the irreducible characters of the symmetric group Sn. We will discuss the structure of the decompositions of a skew partition into a minimal number of border strips. An application to the irreducible characters of Sn will be included. Most of the talk requires no knowledge of symmetric functions or the symmetric group.

Background reading (useful but not necessary for following the talk): my book Enumerative Combinatorics, vol. 2, Exercises 7.59 and 7.66.