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A Note on Trace Polynomial

Department of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China
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Abstract

In this paper, we mainly study the relation of two cyclically reduced words w and w' on the condition they have the same trace polynomial (i.e., tr w=tr w'). 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 = tr w'. 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'.

Keywords

cyclically reduced wordtrace polynomialequivalence

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Tsinghua Science and Technology
Volume 12 Issue 4,
August 2007
Pages 479-484
DOI: 10.1016/S1007-0214(07)70071-8

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Cite this article:
WANG G. A Note on Trace Polynomial. Tsinghua Science and Technology, 2007, 12(4): 479-484. https://doi.org/10.1016/S1007-0214(07)70071-8

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Received: 27 March 2006
Published: 01 August 2007
© Tsinghua University Press 2007