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Volumn 21, Issue 1, 1998, Pages 78-112

Matroids on Partially Ordered Sets

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EID: 0038857112     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1998.0583     Document Type: Article
Times cited : (24)

References (82)
  • 3
    • 0040363107 scopus 로고
    • Axiomatizing matroids by means of the set of non-generators
    • Barnabei M., Nicoletti G. Axiomatizing matroids by means of the set of non-generators. Boll. Un. Mat. Ital. A (5). 17:1980;121-127.
    • (1980) Boll. Un. Mat. Ital. a (5) , vol.17 , pp. 121-127
    • Barnabei, M.1    Nicoletti, G.2
  • 4
    • 0040363117 scopus 로고
    • The symmetric exchange property for poset matroids
    • Barnabei M., Nicoletti G., Pezzoli L. The symmetric exchange property for poset matroids. Adv. Math. 102:1993;230-239.
    • (1993) Adv. Math. , vol.102 , pp. 230-239
    • Barnabei, M.1    Nicoletti, G.2    Pezzoli, L.3
  • 6
    • 0001587385 scopus 로고
    • Abstract linear dependence in lattices
    • Birkhoff G. D. Abstract linear dependence in lattices. Amer. J. Math. 57:1935;800-804.
    • (1935) Amer. J. Math. , vol.57 , pp. 800-804
    • Birkhoff, G.D.1
  • 7
    • 0003347195 scopus 로고
    • Lattice Theory
    • Providence: American Mathematical Society
    • Birkhoff G. D. Lattice Theory, Colloquium Publication 25. 1967;American Mathematical Society, Providence.
    • (1967) Colloquium Publication 25
    • Birkhoff, G.D.1
  • 10
    • 84974189133 scopus 로고
    • Comments on bases in dependence structures
    • Brualdi R. A. Comments on bases in dependence structures. Bull. Austral. Math. Soc. 1:1969;161-167.
    • (1969) Bull. Austral. Math. Soc. , vol.1 , pp. 161-167
    • Brualdi, R.A.1
  • 11
    • 0039765983 scopus 로고
    • Some properties of basic families of subsets
    • Brylawski T. H. Some properties of basic families of subsets. Discrete Math., 6:1973;333-341.
    • (1973) Discrete Math. , vol.6 , pp. 333-341
    • Brylawski, T.H.1
  • 12
    • 84967771322 scopus 로고
    • Modular constructions for combinatorial geometries
    • Brylawski T. H. Modular constructions for combinatorial geometries. Trans. Amer. Math. Soc. 203:1975;1-44.
    • (1975) Trans. Amer. Math. Soc. , vol.203 , pp. 1-44
    • Brylawski, T.H.1
  • 17
    • 0039178473 scopus 로고
    • A remark on an exchange theorem for bases
    • Dawson J. A remark on an exchange theorem for bases. J. Math. Anal. Appl. 62:1978;354-355.
    • (1978) J. Math. Anal. Appl. , vol.62 , pp. 354-355
    • Dawson, J.1
  • 18
    • 0040957243 scopus 로고
    • Dependence relations in a semimodular lattice
    • Dilworth R. P. Dependence relations in a semimodular lattice. Duke Math J. 11:1944;575-587.
    • (1944) Duke Math J. , vol.11 , pp. 575-587
    • Dilworth, R.P.1
  • 20
    • 0001228489 scopus 로고
    • Systems of distinct representatives and linear algebra
    • Edmonds J. Systems of distinct representatives and linear algebra. J. Res. Nat. Bur. Stand. 69B:1967;241-245.
    • (1967) J. Res. Nat. Bur. Stand. , vol.69 , pp. 241-245
    • Edmonds, J.1
  • 22
    • 0002167079 scopus 로고
    • Submodular functions, matroids and certain polyhedra
    • R. Guy. New York: Gordon & Breach
    • Edmonds J. Submodular functions, matroids and certain polyhedra. Guy R. Combinatorial Structures and Their Applications. 1969;69-87 Gordon & Breach, New York.
    • (1969) Combinatorial Structures and Their Applications , pp. 69-87
    • Edmonds, J.1
  • 24
    • 0011312646 scopus 로고
    • Geometries on partially ordered sets
    • Faigle U. Geometries on partially ordered sets. J. Combin. Theory Ser. B. 28:1980;26-51.
    • (1980) J. Combin. Theory Ser. B , vol.28 , pp. 26-51
    • Faigle, U.1
  • 25
    • 0018020371 scopus 로고
    • Polymatroid dependence structure of a set of random variables
    • Fujishige S. Polymatroid dependence structure of a set of random variables. Inform. and Control (Shenyang). 39:1978;55-72.
    • (1978) Inform. and Control (Shenyang) , vol.39 , pp. 55-72
    • Fujishige, S.1
  • 26
    • 0039770916 scopus 로고
    • Decomposing symmetric exchanges in matroid bases
    • Gabow H. Decomposing symmetric exchanges in matroid bases. Math. Prog. 10:1976;271-276.
    • (1976) Math. Prog. , vol.10 , pp. 271-276
    • Gabow, H.1
  • 29
    • 84968494925 scopus 로고
    • A multiple exchange property for bases
    • Greene C. A multiple exchange property for bases. Proc. Amer. Math. Soc. 39:1973;45-50.
    • (1973) Proc. Amer. Math. Soc. , vol.39 , pp. 45-50
    • Greene, C.1
  • 30
    • 84966230805 scopus 로고
    • Another exchange property for bases
    • Greene C. Another exchange property for bases. Proc. Amer. Math. Soc. 46:1974;155-156.
    • (1974) Proc. Amer. Math. Soc. , vol.46 , pp. 155-156
    • Greene, C.1
  • 32
    • 0040363094 scopus 로고
    • Minors in Boolean structure and matroids
    • Guidotti L., Nicoletti G. Minors in Boolean structure and matroids. Ann. Discrete Math. 14:1982;219-224.
    • (1982) Ann. Discrete Math. , vol.14 , pp. 219-224
    • Guidotti, L.1    Nicoletti, G.2
  • 33
    • 84963056434 scopus 로고
    • On representatives of subsets
    • Hall P. On representatives of subsets. J. London Math. Soc. 10:1935;26-30.
    • (1935) J. London Math. Soc. , vol.10 , pp. 26-30
    • Hall, P.1
  • 35
    • 0039770933 scopus 로고
    • Geometry
    • Ontario: University of Waterloo
    • Higgs D. A. Geometry. Lecture Notes. 1966;University of Waterloo, Ontario.
    • (1966) Lecture Notes
    • Higgs, D.A.1
  • 36
    • 84963011761 scopus 로고
    • A note on independence functions and rank
    • Ingleton A. W. A note on independence functions and rank. J. London Math. Soc. 34:1959;49-56.
    • (1959) J. London Math. Soc. , vol.34 , pp. 49-56
    • Ingleton, A.W.1
  • 37
    • 0038485118 scopus 로고
    • Gammoids and transversal matroids
    • Ingleton A. W., Piff M. J. Gammoids and transversal matroids. J. Combin. Theory. 15:1973;51-68.
    • (1973) J. Combin. Theory , vol.15 , pp. 51-68
    • Ingleton, A.W.1    Piff, M.J.2
  • 38
    • 0040957172 scopus 로고
    • Random matroids
    • Knuth D. E. Random matroids. Discrete Math. 12:1975;341-358.
    • (1975) Discrete Math. , vol.12 , pp. 341-358
    • Knuth, D.E.1
  • 39
    • 0001872985 scopus 로고
    • An analysis of the greedy heuristic for independence systems
    • Korte B., Hausmann D. An analysis of the greedy heuristic for independence systems. Ann. Discrete Math. 2:1978;65-74.
    • (1978) Ann. Discrete Math. , vol.2 , pp. 65-74
    • Korte, B.1    Hausmann, D.2
  • 40
    • 84966251058 scopus 로고
    • Alternating basis exchanges in matroids
    • Kung J. P. S. Alternating basis exchanges in matroids. Proc. Amer. Math. Soc. 71:1978;355-358.
    • (1978) Proc. Amer. Math. Soc. , vol.71 , pp. 355-358
    • Kung, J.P.S.1
  • 41
    • 0040957242 scopus 로고
    • On specializations of matroids
    • Kung J. P. S. On specializations of matroids. Stud. Appl. Math. 62:1980;183-187.
    • (1980) Stud. Appl. Math. , vol.62 , pp. 183-187
    • Kung, J.P.S.1
  • 43
    • 0013006286 scopus 로고
    • Oriented matroids and multiply ordered sets
    • Lawrence J. Oriented matroids and multiply ordered sets. Linear Algebra Appl. 48:1982;1-12.
    • (1982) Linear Algebra Appl. , vol.48 , pp. 1-12
    • Lawrence, J.1
  • 44
    • 84963024014 scopus 로고
    • The representation problem for independence functions
    • Lazarson T. 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
  • 45
    • 0001275487 scopus 로고
    • Some interpretations of abstract linear dependence in terms of projective geometry
    • MacLane S. Some interpretations of abstract linear dependence in terms of projective geometry. Amer. J. Math. 58:1936;236-240.
    • (1936) Amer. J. Math. , vol.58 , pp. 236-240
    • MacLane, S.1
  • 46
    • 0039770915 scopus 로고
    • Complementary bases of a matroid
    • Magnanti T. L. Complementary bases of a matroid. Discrete Math. 8:1974;355-361.
    • (1974) Discrete Math. , vol.8 , pp. 355-361
    • Magnanti, T.L.1
  • 47
    • 0040363104 scopus 로고
    • Matroids as the study of geometrical configurations
    • M. Aigner. Dordrecht: Reidel
    • Mason J. H. Matroids as the study of geometrical configurations. Aigner M. Higher Combinatorics. 1977;133-176 Reidel, Dordrecht.
    • (1977) Higher Combinatorics , pp. 133-176
    • Mason, J.H.1
  • 48
    • 84968521094 scopus 로고
    • An exchange theorem for independence structures
    • McDiarmid C. J. M. An exchange theorem for independence structures. Proc. Amer. Math. Soc. 47:1975;513-514.
    • (1975) Proc. Amer. Math. Soc. , vol.47 , pp. 513-514
    • McDiarmid, C.J.M.1
  • 49
    • 0039770914 scopus 로고
    • Application of the notion of independence to combinatorial analysis
    • Mirsky L., Perfect H. Application of the notion of independence to combinatorial analysis. J. Combin. Theory. 2:1967;327-357.
    • (1967) J. Combin. Theory , vol.2 , pp. 327-357
    • Mirsky, L.1    Perfect, H.2
  • 50
    • 0010874033 scopus 로고
    • Semi-modular functions and combinatorial geometries
    • Nguyen H. Q. Semi-modular functions and combinatorial geometries. Trans. Amer. Math. Soc. 238:1978;355-383.
    • (1978) Trans. Amer. Math. Soc. , vol.238 , pp. 355-383
    • Nguyen, H.Q.1
  • 51
    • 52649122986 scopus 로고
    • Generating cryptomorphic axiomatizations of matroids
    • R. Artzy, & I. Vaisman. Berlin: Springer-Verlag
    • Nicoletti G. Generating cryptomorphic axiomatizations of matroids. Artzy R., Vaisman I. Geometry and Differential Geometry. Lecture Notes in Mathematics. 792:1979;110-113 Springer-Verlag, Berlin.
    • (1979) Geometry and Differential Geometry. Lecture Notes in Mathematics , vol.792 , pp. 110-113
    • Nicoletti, G.1
  • 52
    • 0004061262 scopus 로고
    • New York: Oxford University PressOxford Science Publications, The Clarendon Press
    • Oxley J. G. Matroid Theory. 1992;Oxford University PressOxford Science Publications, The Clarendon Press, New York.
    • (1992) Matroid Theory
    • Oxley, J.G.1
  • 53
    • 0040363102 scopus 로고
    • Independence spaces and combinatorial problems
    • Perfect H. Independence spaces and combinatorial problems. Proc. London Math. Soc. 19:1969;17-30.
    • (1969) Proc. London Math. Soc. , vol.19 , pp. 17-30
    • Perfect, H.1
  • 54
    • 0040957227 scopus 로고
    • Independence theory and matroids
    • Perfect H. Independence theory and matroids. Math. Gaz. 65:1981;103-111.
    • (1981) Math. Gaz. , vol.65 , pp. 103-111
    • Perfect, H.1
  • 56
    • 0040957225 scopus 로고
    • Sistemi di indipendenza modulari
    • Pezzoli L. Sistemi di indipendenza modulari. Boll. Un. Mat. Ital. B (5). 18-B:1981;575-590.
    • (1981) Boll. Un. Mat. Ital. B (5) , vol.18 , pp. 575-590
    • Pezzoli, L.1
  • 58
    • 0039770913 scopus 로고
    • On D-complementation
    • Pezzoli L. On D-complementation. Adv. Math. 51:1984;226-239.
    • (1984) Adv. Math. , vol.51 , pp. 226-239
    • Pezzoli, L.1
  • 59
    • 0039770863 scopus 로고
    • Teoria delle matroidi sugli insiemi parzialmente ordinati
    • G. Nicoletti. Publications de l'Institut de Recherche Mathématique Avancée
    • Pezzoli L. Teoria delle matroidi sugli insiemi parzialmente ordinati. Nicoletti G. Publications de l'Institut de Recherche Mathématique Avancée. Actes du 13° Séminaire Lotharingien de Combinatoire. 316:1986;83-104.
    • (1986) Actes du 13° Séminaire Lotharingien de Combinatoire , vol.316 , pp. 83-104
    • Pezzoli, L.1
  • 60
    • 0039770922 scopus 로고
    • The closure lattice of combinatorial schemes
    • Pezzoli L., Ross N. J. The closure lattice of combinatorial schemes. C.N.R. Report. 1990.
    • (1990) C.N.R. Report
    • Pezzoli, L.1    Ross, N.J.2
  • 61
    • 0040957235 scopus 로고
    • Submodular functions and independence structures
    • Pym J. S., Perfect H. Submodular functions and independence structures. J. Math. Anal. Appl. 30:1970;1-31.
    • (1970) J. Math. Anal. Appl. , vol.30 , pp. 1-31
    • Pym, J.S.1    Perfect, H.2
  • 62
    • 17244378946 scopus 로고
    • A theorem on independence relations
    • Rado R. A theorem on independence relations. Quart. J. Math. Oxford. 20:1949;95-104.
    • (1949) Quart. J. Math. Oxford , vol.20 , pp. 95-104
    • Rado, R.1
  • 65
    • 0040363103 scopus 로고
    • Faculty of Actuarial Science, University of Amsterdam
    • A. Schrijver, Submodular Functions, Faculty of Actuarial Science, University of Amsterdam, 1982.
    • (1982) Submodular Functions
    • Schrijver, A.1
  • 66
    • 0040363085 scopus 로고
    • On the points-lines-planes conjecture
    • Seymour P. D. On the points-lines-planes conjecture. J. Combin. Theory Ser. B. 33:1982;17-26.
    • (1982) J. Combin. Theory Ser. B , vol.33 , pp. 17-26
    • Seymour, P.D.1
  • 68
    • 0040363084 scopus 로고
    • A combinatorial generalization of polytopes
    • Todd M. J. A combinatorial generalization of polytopes. J. Combin. Theory Ser. B. 20:1976;229-242.
    • (1976) J. Combin. Theory Ser. B , vol.20 , pp. 229-242
    • Todd, M.J.1
  • 71
    • 0039770862 scopus 로고
    • A basis extension property
    • White N. L. A basis extension property. J. London Math. Soc. 7:1974;662-664.
    • (1974) J. London Math. Soc. , vol.7 , pp. 662-664
    • White, N.L.1
  • 72
    • 0039178405 scopus 로고
    • A unique exchange property for bases
    • White N. L. A unique exchange property for bases. Linear Algebra Appl. 31:1980;81-91.
    • (1980) Linear Algebra Appl. , vol.31 , pp. 81-91
    • White, N.L.1
  • 76
    • 0001587384 scopus 로고
    • On the abstract properties of linear dependence
    • Whitney H. 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
  • 77
    • 0039178403 scopus 로고
    • An exchange theorem for bases of matroids
    • Woodall D. R. An exchange theorem for bases of matroids. J. Combin. Theory. 16:1974;227-228.
    • (1974) J. Combin. Theory , vol.16 , pp. 227-228
    • Woodall, D.R.1
  • 79
    • 21844502862 scopus 로고
    • Axioms for maximal vectors of an oriented matroid: A combinatorial characterization of the regions determined by an arrangement of pseudohyperplanes
    • da Silva I. P. F. Axioms for maximal vectors of an oriented matroid: A combinatorial characterization of the regions determined by an arrangement of pseudohyperplanes. Eur. J. Comb. 16:1995;125-145.
    • (1995) Eur. J. Comb. , vol.16 , pp. 125-145
    • Da Silva, I.P.F.1
  • 81
    • 84968518142 scopus 로고
    • The bracket ring of a combinatorial geometry. I
    • White N. L. The bracket ring of a combinatorial geometry. I. Trans. Am. Math. Soc. 202:1975;79-95.
    • (1975) Trans. Am. Math. Soc. , vol.202 , pp. 79-95
    • White, N.L.1
  • 82
    • 84968512778 scopus 로고
    • The bracket ring of a combinatorial geometry: II: Unimodular geometries
    • White N. L. The bracket ring of a combinatorial geometry: II: Unimodular geometries. Trans. Am. Math. Soc. 214:1975;233-248.
    • (1975) Trans. Am. Math. Soc. , vol.214 , pp. 233-248
    • White, N.L.1


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