#### Vol. 7, No. 4, 2014

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Ethics Statement Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print)
On a state model for the $\mathrm{SO}(2n)$ Kauffman polynomial

### Carmen Caprau, David Heywood and Dionne Ibarra

Vol. 7 (2014), No. 4, 547–563
##### Abstract

François Jaeger presented the two-variable Kauffman polynomial of an unoriented link $L$ as a weighted sum of HOMFLY-PT polynomials of oriented links associated with $L$. Murakami, Ohtsuki and Yamada (MOY) used planar graphs and a recursive evaluation of these graphs to construct a state model for the $sl\left(n\right)$-link invariant (a one-variable specialization of the HOMFLY-PT polynomial). We apply the MOY framework to Jaeger’s work, and construct a state summation model for the $SO\left(2n\right)$ Kauffman polynomial.

##### Keywords
graphs, invariants for knots and links, Kauffman polynomial
##### Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M27, 57M15