Coloring link diagrams by Alexander Quandles

Yongju Bae

doi:10.1142/S0218216512500940

Coloring link diagrams by Alexander Quandles

Yongju Bae

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

10 Scopus citations

Abstract

In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial _L(t) is vanishing, then L admits a non-trivial coloring by any non-trivial Alexander quandle Q, and that if _L(t) = 1, then L admits only the trivial coloring by any Alexander quandle Q, also show that if _L(t) ≠ 0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/( _L(t)).

Original language	English
Article number	1250094
Journal	Journal of Knot Theory and its Ramifications
Volume	21
Issue number	10
DOIs	https://doi.org/10.1142/S0218216512500940
State	Published - Sep 2012

Keywords

Alexander polynomial
Knot
coloring
link
quandle

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10.1142/S0218216512500940

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title = "Coloring link diagrams by Alexander Quandles",

abstract = "In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial L(t) is vanishing, then L admits a non-trivial coloring by any non-trivial Alexander quandle Q, and that if L(t) = 1, then L admits only the trivial coloring by any Alexander quandle Q, also show that if L(t) ≠ 0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/( L(t)).",

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AB - In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial L(t) is vanishing, then L admits a non-trivial coloring by any non-trivial Alexander quandle Q, and that if L(t) = 1, then L admits only the trivial coloring by any Alexander quandle Q, also show that if L(t) ≠ 0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/( L(t)).

KW - Alexander polynomial

KW - Knot

KW - coloring

KW - link

KW - quandle

UR - https://www.scopus.com/pages/publications/84870270124

U2 - 10.1142/S0218216512500940

DO - 10.1142/S0218216512500940

M3 - Article

AN - SCOPUS:84870270124

SN - 0218-2165

VL - 21

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 10

M1 - 1250094

ER -

Coloring link diagrams by Alexander Quandles

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Keywords

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