Isotropic systems and the interlace polynomial
| dc.creator | Ellis-Monaghan, Joanna A. | |
| dc.creator | Sarmiento, Irasema | |
| dc.date | 2006-06-26 | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T07:17:41Z | |
| dc.date.available | 2026-07-07T07:17:41Z | |
| dc.description | Through a series of papers in the 1980's, Bouchet introduced isotropic systems and the Tutte-Martin polynomial of an isotropic system. Then, Arratia, Bollobás, and Sorkin developed the interlace polynomial of a graph in [ABS00] in response to a DNA sequencing application. The interlace polynomial has generated considerable recent attention, with new results including realizing the original interlace polynomial by a closed form generating function expression instead of by the original recursive definition (see Aigner and van der Holst [AvdH04], and Arratia, Bollobás, and Sorkin [ABS04b]). Now, Bouchet [Bou05] recognizes the vertex-nullity interlace polynomial of a graph as the Tutte-Martin polynomial of an associated isotropic system. This suggests that the machinery of isotropic systems may be well-suited to investigating properties of the interlace polynomial. Thus, we present here an alternative proof for the closed form presentation of the vertex-nullity interlace polynomial using the machinery of isotropic systems. This approach both illustrates the intimate connection between the vertex-nullity interlace polynomial and the Tutte-Martin polynomial of an isotropic system and also provides a concrete example of manipulating isotropic systems. We also provide a brief survey of related work. | |
| dc.identifier | https://arxiv.org/abs/math/0606641 | |
| dc.identifier | http://arxiv.org/abs/math/0606641 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114027 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C38, 05C45 | |
| dc.title | Isotropic systems and the interlace polynomial | |
| dc.type | text |