International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 2, Pages 229-237
doi:10.1155/S0161171279000211
On the Alexander polynominals of alternating two-component links
Department of Mathematics, Amherst College, Amherst 01002, Massachusetts, USA
Received 5 September 1978
Copyright © 1979 Mark E. Kidwell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let L be an alternating two-component link with Alexander polynomial Δ(x,y). Then the polynomials (1−x)Δ(x,y) and (1−y)Δ(x,y) are alternating. That is, (1−y)Δ(x,y) can be written as ∑i,jcijxiyj in such a way that (−1)i+jcij≥0.