Abstract of Paper |

*On the Length of the Minimum Solution of Word Equations in One Variable*

by Kensuke Baba, Satoshi Tsuruta, Ayumi Shinohara, and Masayuki Takeda

**Abstract:**

We show the {\em tight upperbound} of the length of the minimum solution of a word equation $L=R$ in one variable, in terms of the differences between the positions of corresponding variable occurrences in $L$ and $R$. By introducing the notion of difference, the proof is obtained from Fine and Wilf's theorem. As a corollary, it implies that the length of the minimum solution is less than $N=\vert L\vert+\vert R\vert$.