多项式Birack模
Polynomial Birack Modules
摘要：
Birack模是代数Z[X]上与有限Birack X相关联的模。在以前的工作中，使用Z mod n上的birack模结构来增强birack计数不变量。本文利用Laurent多项式环Z_n[q，1/q]上的birack模来增强birack计数不变量，为每个X-标号图定义一个定制的Alexander多项式式签名，这些多项式的多重集是birack计数不变量的增强.我们提供的例子表明，新的不变量是强于未增强的birack计数不变量，是不是由广义亚历山大多项式。
英文摘要：
Birack modules are modules over an algebra Z[X] associated to a finite birack X. In previous work, birack module structures on Z mod n were used to enhance the birack counting invariant. In this paper, we use birack modules over Laurent polynomial rings Z_n[q,1/q] to enhance the birack counting invariant, defining a customized Alexander polynomial-style signature for each X-labeled diagram; the multiset of these polynomials is an enhancement of the birack counting invariant. We provide examples to demonstrate that the new invariant is stronger than the unenhanced birack counting invariant and is not determined by the generalized Alexander polynomial.
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