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In the mathematical field of knot theory, the HOMFLY polynomial, sometimes called the HOMFLY-PT polynomial or the generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant in the form of a polynomial of variables ''m'' and ''l''. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One tool used to answer such questions is a knot polynomial, which is computed from a diagram of the knot and can be shown to be an invariant of the knot, i.e. diagrams representing the same knot have the same polynomial. The converse may not be true. The HOMFLY polynomial is one such invariant and it generalizes two polynomials previously discovered, the Alexander polynomial and the Jones polynomial, both of which can be obtained by appropriate substitutions from HOMFLY. The HOMFLY polynomial is also a quantum invariant. The name ''HOMFLY'' combines the initials of its co-discoverers: Jim Hoste, Adrian Ocneanu, Kenneth Millett, Peter J. Freyd, W. B. R. Lickorish, and David N. Yetter. The addition of ''PT'' recognizes independent work carried out by Józef H. Przytycki and Paweł Traczyk. ==Definition== The polynomial is defined using skein relations: : : where are links formed by crossing and smoothing changes on a local region of a link diagram, as indicated in the figure. The HOMFLY polynomial of a link ''L'' that is a split union of two links and is given by : See the page on skein relation for an example of a computation using such relations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「HOMFLY polynomial」の詳細全文を読む スポンサード リンク
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