Alexander polynomialn.

Brit.

/alᵻɡˌzɑːndə pɒlɪˈnəʊmɪəl/,

/alᵻɡˌzandə pɒlɪˈnəʊmɪəl/, U.S.

/æləɡˌzændər pɑliˈnoʊmiəl/,

/æləɡˌzændər pɑləˈnoʊmiəl/

Origin: From a proper name, combined with an English element. Etymons: proper name Alexander , polynomial n.

Etymology: < the name of James Waddell Alexander (1888–1971), U.S. mathematician, who suggested this method of characterizing knots in 1928 ( Trans. Amer. Math. Soc. 30 275) + polynomial n.

Mathematics.

A polynomial in one variable that can be constructed for any knot (based on the number and type of crossings present in a two-dimensional representation of the knot), and is the same for any two knots which are topologically equivalent.Although topologically equivalent knots necessarily have the same Alexander polynomial, knots having the same Alexander polynomial are not necessarily equivalent.

ΚΠ

1932 Amer. Jrnl. Math. 54 453 The polynomial F(x) in section (5) of this paper is also obtained by Burau as the Alexander polynomial of the knot.

1953 Ann. Math. 57 57 The Alexander polynomial of a knot K of multiplicity μ..is an integral polynomial.

1975 Nature 4 Dec. 399/1 Each chain was classified as to its specific topological type by calculating its Alexander polynomial.

2004 P. Cromwell Knots & Links vii. 158 Even though there are infinitely many knots with a given polynomial.., in practice, the Alexander polynomial is a useful tool for distinguishing links.

This is a new entry (OED Third Edition, September 2012; most recently modified version published online December 2021).

单词	alexander polynomial
释义	Alexander polynomialn. Brit. /alᵻɡˌzɑːndə pɒlɪˈnəʊmɪəl/, /alᵻɡˌzandə pɒlɪˈnəʊmɪəl/, U.S. /æləɡˌzændər pɑliˈnoʊmiəl/, /æləɡˌzændər pɑləˈnoʊmiəl/ Origin: From a proper name, combined with an English element. Etymons: proper name Alexander , polynomial n. Etymology: < the name of James Waddell Alexander (1888–1971), U.S. mathematician, who suggested this method of characterizing knots in 1928 ( Trans. Amer. Math. Soc. 30 275) + polynomial n. Mathematics. A polynomial in one variable that can be constructed for any knot (based on the number and type of crossings present in a two-dimensional representation of the knot), and is the same for any two knots which are topologically equivalent.Although topologically equivalent knots necessarily have the same Alexander polynomial, knots having the same Alexander polynomial are not necessarily equivalent. ΚΠ 1932 Amer. Jrnl. Math. 54 453 The polynomial F(x) in section (5) of this paper is also obtained by Burau as the Alexander polynomial of the knot. 1953 Ann. Math. 57 57 The Alexander polynomial of a knot K of multiplicity μ..is an integral polynomial. 1975 Nature 4 Dec. 399/1 Each chain was classified as to its specific topological type by calculating its Alexander polynomial. 2004 P. Cromwell Knots & Links vii. 158 Even though there are infinitely many knots with a given polynomial.., in practice, the Alexander polynomial is a useful tool for distinguishing links. This is a new entry (OED Third Edition, September 2012; most recently modified version published online December 2021). < n.1932
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