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A note on trace polynomial

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1 Author(s)
Wang, Guizhen ; Department of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China

In this paper, we mainly study the relation of two cyclically reduced words wand w' on the condition they have the same trace polynomial (i.e., tr w = trw'). By defining an equivalence relation through such operators on words as inverse, cyclically left shift, and mirror, it is straightforward to get that w∼w' implies tr w = trw'. We show by a counter example that tr w = tr w' does not imply w ∼ w'. And in two special cases, we prove that tr w = tr w' if and only if w ∼ w'.

Published in:

Tsinghua Science and Technology  (Volume:12 ,  Issue: 4 )