메뉴 건너뛰기




Volumn 302, Issue 1-3, 2005, Pages 285-296

Recent work in matroid representation theory

Author keywords

Finite field; Matroid representation; Matroids

Indexed keywords

OPTIMIZATION; PROBLEM SOLVING; TOPOLOGY;

EID: 27744591063     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2004.07.039     Document Type: Conference Paper
Times cited : (14)

References (37)
  • 1
    • 0346321988 scopus 로고
    • On Reid's characterization of the ternary matroids
    • R.E. Bixby On Reid's characterization of the ternary matroids J. Combin. Theory Ser. B 26 1979 174 204
    • (1979) J. Combin. Theory Ser. B , vol.26 , pp. 174-204
    • Bixby, R.E.1
  • 2
    • 0002681234 scopus 로고
    • A class of geometric lattices based on finite groups
    • erratum: J. Combin. Theory Ser. B 15 (1973) 211
    • T.A. Dowling A class of geometric lattices based on finite groups J. Combin. Theory Ser. B 14 1973 61 86; erratum: J. Combin. Theory Ser. B 15 (1973) 211.
    • (1973) J. Combin. Theory Ser. B , vol.14 , pp. 61-86
    • Dowling, T.A.1
  • 3
    • 0002383986 scopus 로고
    • A q-analog of the partition lattice
    • J.N. Srivastava North-Holland Amsterdam*et al.
    • T.A. Dowling A q -analog of the partition lattice J.N. Srivastava A Survey of Combinatorial Theory 1973 North-Holland Amsterdam
    • (1973) A Survey of Combinatorial Theory
    • Dowling, T.A.1
  • 6
    • 0036211275 scopus 로고    scopus 로고
    • Branch-width and well-quasi-ordering in matroids and graphs
    • J. Geelen, A.M.H. Gerards, and G. Whittle Branch-width and well-quasi-ordering in matroids and graphs J. Combin. Theory Ser. B 84 2002 270 290
    • (2002) J. Combin. Theory Ser. B , vol.84 , pp. 270-290
    • Geelen, J.1    Gerards, A.M.H.2    Whittle, G.3
  • 11
    • 0035185270 scopus 로고    scopus 로고
    • Matroid 4-connectivity: A deletion contraction theorem
    • J. Geelen, and G. Whittle Matroid 4-connectivity: a deletion contraction theorem J. Combin. Theory Ser. B 83 2001 15 37
    • (2001) J. Combin. Theory Ser. B , vol.83 , pp. 15-37
    • Geelen, J.1    Whittle, G.2
  • 13
    • 0000296859 scopus 로고
    • A short proof of Tutte's characterization of totally unimodular matrices
    • A.M.H. Gerards A short proof of Tutte's characterization of totally unimodular matrices Linear Algebra Appl. 114/115 1989 207 212
    • (1989) Linear Algebra Appl. , vol.114-115 , pp. 207-212
    • Gerards, A.M.H.1
  • 14
    • 33745959090 scopus 로고
    • On the uniqueness of matroid representation over GF(4)
    • J. Kahn On the uniqueness of matroid representation over GF (4 ) Bull. London Math. Soc. 20 1988 5 10
    • (1988) Bull. London Math. Soc. , vol.20 , pp. 5-10
    • Kahn, J.1
  • 15
    • 0011416536 scopus 로고
    • Varieties of combinatorial geometries
    • J. Kahn, and J.P.S. Kung Varieties of combinatorial geometries Trans. Amer. Math. Soc. 271 1982 485 499
    • (1982) Trans. Amer. Math. Soc. , vol.271 , pp. 485-499
    • Kahn, J.1    Kung, J.P.S.2
  • 17
    • 84963024014 scopus 로고
    • The representation problem for independence functions
    • T. Lazarson The representation problem for independence functions J. London Math. Soc. 33 1958 21 25
    • (1958) J. London Math. Soc. , vol.33 , pp. 21-25
    • Lazarson, T.1
  • 18
    • 0004061262 scopus 로고
    • Oxford University Press New York
    • J.G. Oxley Matroid Theory 1992 Oxford University Press New York
    • (1992) Matroid Theory
    • Oxley, J.G.1
  • 21
    • 0030187155 scopus 로고    scopus 로고
    • On inequivalent representations of matroids over finite fields
    • J.G. Oxley, D.L. Vertigan, and G.P. Whittle On inequivalent representations of matroids over finite fields J. Combin. Theory Ser. B 67 1996 325 343
    • (1996) J. Combin. Theory Ser. B , vol.67 , pp. 325-343
    • Oxley, J.G.1    Vertigan, D.L.2    Whittle, G.P.3
  • 22
    • 0348050580 scopus 로고    scopus 로고
    • Conjectures on matroids representable over GF(3) and other fields
    • J.E. Bonin, J.G. Oxley, B. Servatius (Eds.), Matroid Theory
    • J.G. Oxley, D.L. Vertigan, G.P. Whittle, Conjectures on matroids representable over GF (3 ) and other fields, in: J.E. Bonin, J.G. Oxley, B. Servatius (Eds.), Matroid Theory, Contemporary Mathematics, vol. 197, 1996, pp. 411-412.
    • (1996) Contemporary Mathematics , vol.197 , pp. 411-412
    • Oxley, J.G.1    Vertigan, D.L.2    Whittle, G.P.3
  • 26
    • 0011518480 scopus 로고
    • Combinatorial theory, old and new
    • Nice, September 1970, Gauthier, Chichester
    • G.-C. Rota, Combinatorial theory, old and new, in: Proceedings of International Congress of Mathematics, Nice, September 1970, Gauthier, Chichester, 1970, pp. 229-233.
    • (1970) Proceedings of International Congress of Mathematics , pp. 229-233
    • Rota, G.-C.1
  • 27
    • 0030160058 scopus 로고    scopus 로고
    • Partial fields and matroid representation
    • C. Semple, and G. Whittle Partial fields and matroid representation Adv. Appl. Math. 17 1996 184 208
    • (1996) Adv. Appl. Math. , vol.17 , pp. 184-208
    • Semple, C.1    Whittle, G.2
  • 28
    • 0001523212 scopus 로고
    • Matroid representation over GF(3)
    • P.D. Seymour Matroid representation over GF (3 ) J. Combin. Theory Ser. B 26 1979 159 173
    • (1979) J. Combin. Theory Ser. B , vol.26 , pp. 159-173
    • Seymour, P.D.1
  • 29
    • 49149147896 scopus 로고
    • Decomposition of regular matroids
    • P.D. Seymour Decomposition of regular matroids J. Combin. Theory Ser. B 28 1980 305 359
    • (1980) J. Combin. Theory Ser. B , vol.28 , pp. 305-359
    • Seymour, P.D.1
  • 30
    • 51249186893 scopus 로고
    • Recognizing graphic matroids
    • P.D. Seymour Recognizing graphic matroids Combinatorica 1 1981 75 78
    • (1981) Combinatorica , vol.1 , pp. 75-78
    • Seymour, P.D.1
  • 31
    • 84968508683 scopus 로고
    • A homotopy theorem for matroids, I, II
    • W.T. Tutte A homotopy theorem for matroids, I, II Trans. Amer. Math. Soc. 88 1958 144 174
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 144-174
    • Tutte, W.T.1
  • 32
    • 0000444115 scopus 로고
    • Connectivity in matroids
    • W.T. Tutte Connectivity in matroids Canad. J. Math. 18 1966 1301 1324
    • (1966) Canad. J. Math. , vol.18 , pp. 1301-1324
    • Tutte, W.T.1
  • 34
    • 0001587384 scopus 로고
    • On the abstract properties of linear dependence
    • H. Whitney On the abstract properties of linear dependence Amer. J. Math. 57 1935 509 533
    • (1935) Amer. J. Math. , vol.57 , pp. 509-533
    • Whitney, H.1
  • 35
    • 0001546326 scopus 로고
    • A characterisation of the matroids representable over GF(3) and the rationals
    • G.P. Whittle A characterisation of the matroids representable over GF (3 ) and the rationals J. Combin. Theory Ser. B 65 1995 222 261
    • (1995) J. Combin. Theory Ser. B , vol.65 , pp. 222-261
    • Whittle, G.P.1
  • 36
    • 0039090569 scopus 로고    scopus 로고
    • On matroids representable over GF(3) and other fields
    • G.P. Whittle On matroids representable over GF (3 ) and other fields Trans. Amer. Math. Soc. 349 1997 579 603
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 579-603
    • Whittle, G.P.1
  • 37
    • 0002766745 scopus 로고
    • Biased graphs. II. the three matroids
    • T. Zaslavsky Biased graphs. II. The three matroids J. Combin. Theory Ser. B 51 1991 46 72
    • (1991) J. Combin. Theory Ser. B , vol.51 , pp. 46-72
    • Zaslavsky, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.