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 Δ L (t) is vanishing, then L admits a non-trivial coloring by any non-trivial Alexander quandle Q, and that if Δ L (t) = 1, then L admits only the trivial coloring by any Alexander quandle Q, also show that if Δ L (t) ≠ 0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/(Δ L (t)).