In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.
The Conway potential function （CPF） for colored links is a convenient version of the multi- variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In pa...The Conway potential function （CPF） for colored links is a convenient version of the multi- variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway＇s ＂smoothing of crossings＂ is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra PnBn, where Bn is a braid group and Pn is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities
文摘In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.
文摘The Conway potential function （CPF） for colored links is a convenient version of the multi- variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway＇s ＂smoothing of crossings＂ is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra PnBn, where Bn is a braid group and Pn is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.
