References analysis of the Wikipedia article "Matroid" in the English version

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Oxley (1992) is a standard source for basic definitions and results about matroids; Welsh (1976) is an older standard source.

See the appendix by Brylawski in White (1986), pp. 298–302, for a list of matroid axiom systems that are equivalent.

Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002. Welsh, D.J.A. (1976). Matroid Theory. L.M.S. Monographs. Vol. 8. Academic Press. ISBN 978-0-12-744050-7. Zbl 0343.05002. White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

Although it was perhaps implied, Whitney (1935) did not include an axiom requiring at least one subset to be independent.

Whitney, Hassler (1935). "On the abstract properties of linear dependence". American Journal of Mathematics. 57 (3): 509–533. doi:10.2307/2371182. hdl:10338.dmlcz/100694. JSTOR 2371182. MR 1507091. — Reprinted in Kung (1986), pp. 55–79

Oxley (1992), p. 13 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), pp. 115 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 100 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), pp. 46–48 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 215 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 216 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 52 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 347 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 128 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 26 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 64 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Nishimura & Kuroda (2009) Nishimura, Hirokazu; Kuroda, Susumu, eds. (2009). A lost mathematician, Takeo Nakasawa: The forgotten father of matroid theory. Basel, CH: Birkhäuser Verlag. doi:10.1007/978-3-7643-8573-6. ISBN 978-3-7643-8572-9. MR 2516551. Zbl 1163.01001.

ams.org

"Solving Rota's conjecture" (PDF). Notices of the American Mathematical Society: 736–743. Aug 17, 2014.

archive.org (Global: 6^th place; English: 6^th place)

Oxley (1992) is a standard source for basic definitions and results about matroids; Welsh (1976) is an older standard source.

See the appendix by Brylawski in White (1986), pp. 298–302, for a list of matroid axiom systems that are equivalent.

White (1987), pp. 72–97 White, Neil, ed. (1987). Combinatorial Geometries. Encyclopedia of Mathematics and its Applications. Vol. 29. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-33339-9. Zbl 0626.00007 – via Internet Archive (archive.org).

White (1986), p. 32 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 105 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 131 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 224 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 139 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 140 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 150 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), pp. 146–147 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 130 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1986), p. 110 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

White (1987), p. 127 White, Neil, ed. (1987). Combinatorial Geometries. Encyclopedia of Mathematics and its Applications. Vol. 29. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-33339-9. Zbl 0626.00007 – via Internet Archive (archive.org).

White (1987), p. 120 White, Neil, ed. (1987). Combinatorial Geometries. Encyclopedia of Mathematics and its Applications. Vol. 29. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-33339-9. Zbl 0626.00007 – via Internet Archive (archive.org).

White (1987), p. 123 White, Neil, ed. (1987). Combinatorial Geometries. Encyclopedia of Mathematics and its Applications. Vol. 29. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-33339-9. Zbl 0626.00007 – via Internet Archive (archive.org).

White (1987), p. 124 White, Neil, ed. (1987). Combinatorial Geometries. Encyclopedia of Mathematics and its Applications. Vol. 29. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-33339-9. Zbl 0626.00007 – via Internet Archive (archive.org).

White (1987), p. 126 White, Neil, ed. (1987). Combinatorial Geometries. Encyclopedia of Mathematics and its Applications. Vol. 29. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-33339-9. Zbl 0626.00007 – via Internet Archive (archive.org).

White (1986), p. 260 White, Neil, ed. (1986). Theory of Matroids. Encyclopedia of Mathematics and its Applications. Vol. 26. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-30937-0. Zbl 0579.00001 – via Internet Archive (archive.org).

doi.org (Global: 2^nd place; English: 2^nd place)

Although it was perhaps implied, Whitney (1935) did not include an axiom requiring at least one subset to be independent.

A fine example is A.M.H. Gerards' short proof (Gerards (1989)) of Tutte's characterization of regular matroids. Gerards, A.M.H. (1989). "A short proof of Tutte's characterization of totally unimodular matrices". Linear Algebra and Its Applications. 114–115: 207–212. doi:10.1016/0024-3795(89)90461-8.

Neel & Neudauer (2009) Neel, David L.; Neudauer, Nancy A. (2009). "Matroids you have known" (PDF). Mathematics Magazine. 82 (1): 26–41. doi:10.4169/193009809x469020. Archived from the original (PDF) on 13 February 2022. Retrieved 4 October 2014 – via Mathematical Association of America (maa.org).

Zaslavsky (1994) Zaslavsky, Thomas (1994). "Frame matroids and biased graphs". European Journal of Combinatorics. 15 (3): 303–307. doi:10.1006/eujc.1994.1034. ISSN 0195-6698. Zbl 0797.05027.

Bérczi, Kristóf; Jánosik, Áron; Mátravölgyi, Bence (2026). "Cyclic Ordering of Split Matroids". The Electronic Journal of Combinatorics. 33 (1). P1.20. doi:10.37236/13537.

Kajitani, Yoji; Ueno, Shuichi; Miyano, Hiroshi (1988). "Ordering of the elements of a matroid such that its consecutive w elements are independent". Discrete Mathematics. 72 (1–3): 187–194. doi:10.1016/0012-365X(88)90209-9.

Gabow, Harold N. (1976). "Decomposing symmetric exchanges in matroid bases". Mathematical Programming. 10 (1): 271–276. doi:10.1007/BF01580672.

hdl.handle.net (Global: 66^th place; English: 34^th place)

Although it was perhaps implied, Whitney (1935) did not include an axiom requiring at least one subset to be independent.

jstor.org (Global: 23^rd place; English: 15^th place)

Although it was perhaps implied, Whitney (1935) did not include an axiom requiring at least one subset to be independent.

zbmath.org (Global: 2,089^th place; English: 1,141^st place)

Oxley (1992) is a standard source for basic definitions and results about matroids; Welsh (1976) is an older standard source.

See the appendix by Brylawski in White (1986), pp. 298–302, for a list of matroid axiom systems that are equivalent.

Welsh (1976, pp. 7–9), Section 1.2, "Axiom Systems for a Matroid". Welsh, D.J.A. (1976). Matroid Theory. L.M.S. Monographs. Vol. 8. Academic Press. ISBN 978-0-12-744050-7. Zbl 0343.05002.

Welsh (1976, pp. 21–22), Section 1.8, "Closed sets = Flats = Subspaces". Welsh, D.J.A. (1976). Matroid Theory. L.M.S. Monographs. Vol. 8. Academic Press. ISBN 978-0-12-744050-7. Zbl 0343.05002.

Welsh (1976, pp. 38–39), Section 2.2, "The Hyperplanes of a Matroid". Welsh, D.J.A. (1976). Matroid Theory. L.M.S. Monographs. Vol. 8. Academic Press. ISBN 978-0-12-744050-7. Zbl 0343.05002.

Oxley (1992), p. 13 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), pp. 115 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 100 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), pp. 46–48 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 215 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 216 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 52 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 347 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 128 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Zaslavsky (1994) Zaslavsky, Thomas (1994). "Frame matroids and biased graphs". European Journal of Combinatorics. 15 (3): 303–307. doi:10.1006/eujc.1994.1034. ISSN 0195-6698. Zbl 0797.05027.

Oxley (1992), p. 26 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Oxley (1992), p. 64 Oxley, James (1992). Matroid Theory. Oxford, UK: Oxford University Press. ISBN 978-0-19-853563-8. MR 1207587. Zbl 0784.05002.

Matroid (English Wikipedia)

ams.org (Global: 434^th place; English: 249^th place)

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ams.org

archive.org (Global: 6^th place; English: 6^th place)

birs.ca (Global: low place; English: low place)

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doi.org (Global: 2^nd place; English: 2^nd place)

hdl.handle.net (Global: 66^th place; English: 34^th place)

jstor.org (Global: 23^rd place; English: 15^th place)

maa.org (Global: 4,358^th place; English: 2,907^th place)

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zbmath.org (Global: 2,089^th place; English: 1,141^st place)

Matroid (English Wikipedia)

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

ams.org

archive.org (Global: 6th place; English: 6th place)

birs.ca (Global: low place; English: low place)

books.google.com (Global: 3rd place; English: 3rd place)

doi.org (Global: 2nd place; English: 2nd place)

hdl.handle.net (Global: 66th place; English: 34th place)

jstor.org (Global: 23rd place; English: 15th place)

maa.org (Global: 4,358th place; English: 2,907th place)

maplesoft.com (Global: low place; English: low place)

web.archive.org (Global: 1st place; English: 1st place)

worldcat.org (Global: 4th place; English: 4th place)

search.worldcat.org

zbmath.org (Global: 2,089th place; English: 1,141st place)

ams.org (Global: 434^th place; English: 249^th place)

archive.org (Global: 6^th place; English: 6^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

doi.org (Global: 2^nd place; English: 2^nd place)

hdl.handle.net (Global: 66^th place; English: 34^th place)

jstor.org (Global: 23^rd place; English: 15^th place)

maa.org (Global: 4,358^th place; English: 2,907^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

worldcat.org (Global: 4^th place; English: 4^th place)

zbmath.org (Global: 2,089^th place; English: 1,141^st place)