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

Access to Document

10.1016/S1007-0214(07)70071-8

Cite this

@article{6cd0d3fa7b3e439ebcaf81b1a36d1bca,

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.",

keywords = "cyclically reduced word, equivalence, trace polynomial",

author = "Guizhen Wang",

year = "2007",

month = aug,

doi = "10.1016/S1007-0214(07)70071-8",

language = "English",

volume = "12",

pages = "479--484",

journal = "Tsinghua Science and Technology",

issn = "1007-0214",

publisher = "Tsinghua University",

number = "4",

}

TY - JOUR

T1 - A Note on Trace Polynomial

AU - Wang, Guizhen

PY - 2007/8

Y1 - 2007/8

N2 - 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.

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 - http://www.scopus.com/inward/record.url?scp=34447624851&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:34447624851

SN - 1007-0214

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

Access to Document

Other files and links

Fingerprint

Cite this