Yamanouchi Words¶

A right (respectively left) Yamanouchi word on a completely ordered alphabet, for instance [1,2,...,n], is a word math such that any right (respectively left) factor of math contains more entries math than math. For example, the word [2, 3, 2, 2, 1, 3, 1, 2, 1, 1] is a right Yamanouchi one.

The evaluation of a word math encodes the number of occurrences of each letter of math. In the case of Yamanouchi words, the evaluation is a partition. For example, the word [2, 3, 2, 2, 1, 3, 1, 2, 1, 1] has evaluation [4, 4, 2].

Yamanouchi words can be useful in the computation of Littlewood-Richardson coefficients $c_{\lambda, \mu}^\nu$ . According to the Littlewood-Richardson rule, $c_{\lambda, \mu}^\nu$ is the number of skew tableaux of shape $\nu / \lambda$ and evaluation $\mu$ , whose row readings are Yamanouchi words.

Previous topic

Restricted growth arrays

Next topic

Paths in Directed Acyclic Graphs

This Page