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 $N=\vert L\vert+\vert R\vert$.