A Note on Trace Polynomial

Guizhen Wang

doi:10.1016/S1007-0214(07)70071-8

A Note on Trace Polynomial

Guizhen Wang^*

^*Corresponding author for this work

School of Computer Science and Technology

Research output: Contribution to journal › Article › peer-review

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 ∼ ^wimplies 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.

Original language	English
Pages (from-to)	479-484
Number of pages	6
Journal	Tsinghua Science and Technology
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/S1007-0214(07)70071-8
Publication status	Published - Aug 2007

Keywords

cyclically reduced word
equivalence
trace polynomial

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10.1016/S1007-0214(07)70071-8

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title = "A Note on Trace Polynomial",

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 ∼ wimplies 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.",

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AB - 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 ∼ wimplies 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.

KW - cyclically reduced word

KW - equivalence

KW - trace polynomial

UR - https://www.scopus.com/pages/publications/34447624851

U2 - 10.1016/S1007-0214(07)70071-8

DO - 10.1016/S1007-0214(07)70071-8

M3 - Article

AN - SCOPUS:34447624851

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VL - 12

SP - 479

EP - 484

JO - Tsinghua Science and Technology

JF - Tsinghua Science and Technology

IS - 4

ER -

A Note on Trace Polynomial

Abstract

Keywords

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