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Link Polynomials of Higher Order
Author(s) -
Rong Yongwu
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610796004681
Subject(s) - homfly polynomial , mathematics , skein , order (exchange) , alexander polynomial , polynomial , skein relation , bracket polynomial , pure mathematics , combinatorics , knot theory , matrix polynomial , knot (papermaking) , mathematical analysis , alternating polynomial , square free polynomial , materials science , finance , economics , composite material
In this paper, we study certain polynomial invariants of links (singular or non‐singular) that are related to the Homfly polynomial and Vassiliev's invariants. The Homfly polynomial H L [ 3 ] (also known as the Flypmoth polynomial) satisfies the well‐known skein relation x H L ++ y H L −+ z H L 0= 0. The Vassiliev invariants [ 1 , 2 ] (of order 1) satisfy the relationsV L ×= V L +− V L −andV L × ×= 0. The invariants that we study satisfy the skein relationsP L ×= x P L ++ y P L −+ z P L 0and P L × ×= 0.