Border strips, snakes, and codes of skew partitionsRichard StanleyMIT
September 19,

ABSTRACT


Border strips and snakes are certain subsets of the Young diagram of a skew partition $\lambda/\mu$. Both are closely related to a certain binary sequence code$(\lambda/\mu)$ which encodes $\lambda/\mu$ in a convenient way. The theory of border strips is highly developed and is intimately connected to ordinary and modular characters of the symmetric group $S_n$, as well as to more recent work on noncommutative symmetric functions, Fock space representations, etc. We will briefly survey some of this subject and then discuss new results concerning the decompositions of $\lambda/\mu$ into a \emph{minimal} number of border strips. No knowledge of representation theory will be assumed. BACKGROUND READING: R. Stanley, \emph{Enumerative Combinatorics}, vol.\ 2, Exercises 7.59 and 7.66. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

