Rim hook

A rim hook, or border strip, is a connected skew Young diagram containing no

2 \times 2

square. Its leg length is one less than its number of occupied rows.

Table of contents
- Border-strip tableau Rim hook

Border-strip tableau ( $μ = λ^{(0)} \subseteq \dots \subseteq λ^{(ℓ)} = λ$ )

 0  0

For a type

α

, each successive difference is a rim hook of size

α_{i}

; zero parts give empty differences of height zero. Label its cells by

i

. Such fillings are weakly increasing along rows and columns, and the height is the sum of the occupied strips' numbers of rows minus one. Empty parts are omitted from the associated product of positive power sums; the finite-variable degree-zero power sum is not inserted.