The bracket polynomial of the Celtic link shadow \(CK_4^{2n}\)

We derive the Kauffman bracket polynomial for the shadow of the Celtic link \(CK_4^{2n}\) using two complementary approaches. The first approach uses a recursive relation within the Celtic framework of Gross and Tucker, based on diagrammatic identities. The second approach makes use of a 4-tangle algebraic framework: a fundamental tangle is concatenated with itself \(n\) times to form an iterated composite tangle, and the Kauffman bracket polynomial is computed by decomposing the state space with respect to the basis elements of the 4-strand diagram monoid.

Recommended citation: Franck Ramaharo (2025), "The bracket polynomial of the Celtic link shadow \(CK_4^{2n}\)", arXiv.org e-Print archive, arXiv:2508.10410 [math.GT].
Download Paper