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Volumn 171, Issue 1-3, 1997, Pages 191-200

Bideterminants, arborescences and extension of the Matrix-Tree Theorem to semirings

Author keywords

Arborescences in graphs; Bideterminants; Linear algebra in semirings; Path algebras; Rooted directed trees

Indexed keywords


EID: 0040560511     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(96)00015-5     Document Type: Article
Times cited : (18)

References (11)
  • 1
    • 0011497784 scopus 로고
    • Über eine der interpolation entsprechende darstellung der eliminations-résultante
    • C.W. Borchardt, Über eine der Interpolation entsprechende Darstellung der Eliminations-Résultante, J. Reine Angew. Math. 57 (1860) 111-121.
    • (1860) J. Reine Angew. Math. , vol.57 , pp. 111-121
    • Borchardt, C.W.1
  • 2
    • 0001217760 scopus 로고
    • A combinatorial proof of the all minors Matrix-Tree theorem
    • S. Chaiken, A combinatorial proof of the All Minors Matrix-Tree Theorem, SIAM J. Algebraic Discrete Methods 3 (1982) 319-329.
    • (1982) SIAM J. Algebraic Discrete Methods , vol.3 , pp. 319-329
    • Chaiken, S.1
  • 3
    • 0002680234 scopus 로고
    • Valeurs propres et vecteurs propres dans les dioïdes, et leurs interprétations en théorie des graphes
    • M. Gondran and M. Minoux, Valeurs propres et vecteurs propres dans les dioïdes, et leurs interprétations en théorie des graphes, Bull. Direction Etudes Recherches EDF, Sér. C(2) (1977) 25-41.
    • (1977) Bull. Direction Etudes Recherches EDF, Sér. C , Issue.2 , pp. 25-41
    • Gondran, M.1    Minoux, M.2
  • 5
    • 0000905183 scopus 로고
    • Linear algebra in dioïds. A survey of recent results
    • M. Gondran and M. Minoux, Linear algebra in dioïds. A survey of recent results, Ann. Discrete Math. 9 (1984) 147-164.
    • (1984) Ann. Discrete Math. , vol.9 , pp. 147-164
    • Gondran, M.1    Minoux, M.2
  • 8
    • 0011615213 scopus 로고
    • Line-digraphs, arborescences and theorems of Tutte and Knuth
    • J.B. Orlin, Line-digraphs, arborescences and theorems of Tutte and Knuth, J. Combin. Theory Ser. B 25 (1978) 187-198.
    • (1978) J. Combin. Theory Ser. B , vol.25 , pp. 187-198
    • Orlin, J.B.1
  • 9
    • 0038015710 scopus 로고
    • A combinatorial proof of the Cayley-Hamilton theorem
    • M. Straubing, A combinatorial proof of the Cayley-Hamilton theorem, Discrete Math. 43 (1983) 273-279.
    • (1983) Discrete Math. , vol.43 , pp. 273-279
    • Straubing, M.1
  • 10
    • 84946454140 scopus 로고
    • The dissection of equilateral triangles into equilateral triangles
    • W.T. Tutte, The dissection of equilateral triangles into equilateral triangles, Proc. Cambridge Philos. Soc. 44 (1948) 463-482.
    • (1948) Proc. Cambridge Philos. Soc. , vol.44 , pp. 463-482
    • Tutte, W.T.1
  • 11
    • 0001772282 scopus 로고
    • A combinatorial approach to matrix algebra
    • D. Zeilberger, A combinatorial approach to matrix algebra, Discrete Math. 56 (1985) 61-72.
    • (1985) Discrete Math. , vol.56 , pp. 61-72
    • Zeilberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.