# 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.

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