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 S_n. 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 S_n 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.