matroidn.

Brit.

/ˈmeɪtrɔɪd/, U.S.

/ˈmeɪtrɔɪd/

Origin: Formed within English, by derivation. Etymons: matrix n., -oid suffix.

Etymology: < matr- (in matrix n.; compare sense 7a at that entry) + -oid suffix.

Mathematics.

A mathematical entity consisting of a finite set E together with a collection ℐ of subsets of E such that (i) the empty set is a member of ℐ, (ii) any subset of a member of ℐ is also a member of ℐ, and (iii) if two subsets I₁ and I₂ are in ℐ, where the cardinality of I₁ is less than that of I₂, then there exists an element e that is in I₂ but not I₁ such that the union of I₁ with {e} is also an element of ℐ.The definition of the collection of subsets generalizes the notion of mathematical independence in linear algebra and graph theory. A basic example of a matroid is E being the set of rows of a matrix, and each subset in ℐ consisting of a number of linearly independent rows.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set

set1857

interval1902

intersection1909

union1912

lattice1933

matroid1935

closure1937

Steiner triple or triplet system1939

recursive set1943

convex hull1951

power set1953

convex envelope1964

Steiner system1966

Julia set1976

Mandelbrot set1984

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets

tantipartite1858

connected1893

measurable1901

ordered1901

well-ordered1901

null1903

empty1905

closed1909

orthonormal1928

matroid1935

recursively enumerable1936

simple1936

disjoint1937

partially ordered1941

1935 H. Whitney in Amer. Jrnl. Math. 57 509 Let us call a system obeying (a) and (b) a ‘matroid’. The present paper is devoted to a study of the elementary properties of matroids.

1960 Proc. Amer. Math. Soc. 11 909 If we can obtain graphs corresponding to the Y-components of a graphic matroid M we can construct from them a graph corresponding to M.

1992 J. G. Oxley Matroid Theory i. 7 A characteristic of matroids is that they can be defined in many different but equivalent ways.

This entry has been updated (OED Third Edition, March 2001; most recently modified version published online March 2022).

单词	matroid
释义	matroidn. Brit. /ˈmeɪtrɔɪd/, U.S. /ˈmeɪtrɔɪd/ Origin: Formed within English, by derivation. Etymons: matrix n., -oid suffix. Etymology: < matr- (in matrix n.; compare sense 7a at that entry) + -oid suffix. Mathematics. A mathematical entity consisting of a finite set E together with a collection ℐ of subsets of E such that (i) the empty set is a member of ℐ, (ii) any subset of a member of ℐ is also a member of ℐ, and (iii) if two subsets I₁ and I₂ are in ℐ, where the cardinality of I₁ is less than that of I₂, then there exists an element e that is in I₂ but not I₁ such that the union of I₁ with {e} is also an element of ℐ.The definition of the collection of subsets generalizes the notion of mathematical independence in linear algebra and graph theory. A basic example of a matroid is E being the set of rows of a matrix, and each subset in ℐ consisting of a number of linearly independent rows. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set set1857 interval1902 intersection1909 union1912 lattice1933 matroid1935 closure1937 Steiner triple or triplet system1939 recursive set1943 convex hull1951 power set1953 convex envelope1964 Steiner system1966 Julia set1976 Mandelbrot set1984 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets tantipartite1858 connected1893 measurable1901 ordered1901 well-ordered1901 null1903 empty1905 closed1909 orthonormal1928 matroid1935 recursively enumerable1936 simple1936 disjoint1937 partially ordered1941 1935 H. Whitney in Amer. Jrnl. Math. 57 509 Let us call a system obeying (a) and (b) a ‘matroid’. The present paper is devoted to a study of the elementary properties of matroids. 1960 Proc. Amer. Math. Soc. 11 909 If we can obtain graphs corresponding to the Y-components of a graphic matroid M we can construct from them a graph corresponding to M. 1992 J. G. Oxley Matroid Theory i. 7 A characteristic of matroids is that they can be defined in many different but equivalent ways. This entry has been updated (OED Third Edition, March 2001; most recently modified version published online March 2022). < n.1935
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