TY - JOUR
T1 - Coloring link diagrams by Alexander Quandles
AU - Bae, Yongju
PY - 2012/9
Y1 - 2012/9
N2 - 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)).
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 - http://www.scopus.com/inward/record.url?scp=84870270124&partnerID=8YFLogxK
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 -