We introduce the Parikh-de-Bruijn grid, a graph whose vertices arefixed-order Parikh vectors, and whose edges are given by a simple shiftoperation. This graph gives structural insight into the nature of sets ofParikh vectors as well as that of the Parikh set of a given string. We show itsutility by proving some results on Parikh-de-Bruijn strings, the abelian analogof de-Bruijn sequences.
On the Parikh-de-Bruijn grid
Zsuzsanna Lipták;
2017-01-01
Abstract
We introduce the Parikh-de-Bruijn grid, a graph whose vertices arefixed-order Parikh vectors, and whose edges are given by a simple shiftoperation. This graph gives structural insight into the nature of sets ofParikh vectors as well as that of the Parikh set of a given string. We show itsutility by proving some results on Parikh-de-Bruijn strings, the abelian analogof de-Bruijn sequences.
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