Let L be an alternating link and be its reduced (or proper) alternating diagram. Let w() denote the writhe of , i.e. the number of positive crossings minus the number of negative crossings. Let VL(t) be the Jones polynomial of L . Let dmaxVL(t) and dminVL(t) denote the maximal and minimal degrees of VL(t), respectively. Furthermore, let σ(L) be the signature of L .
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