Hereditary circuit spaces

V. W. Bryant; J. E. Dawson; Hazel Perfect

Compositio Mathematica (1978)

  • Volume: 37, Issue: 3, page 339-351
  • ISSN: 0010-437X

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Bryant, V. W., Dawson, J. E., and Perfect, Hazel. "Hereditary circuit spaces." Compositio Mathematica 37.3 (1978): 339-351. <http://eudml.org/doc/89387>.

@article{Bryant1978,
author = {Bryant, V. W., Dawson, J. E., Perfect, Hazel},
journal = {Compositio Mathematica},
keywords = {Circuit Spaces; Independence Spaces Matroids},
language = {eng},
number = {3},
pages = {339-351},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Hereditary circuit spaces},
url = {http://eudml.org/doc/89387},
volume = {37},
year = {1978},
}

TY - JOUR
AU - Bryant, V. W.
AU - Dawson, J. E.
AU - Perfect, Hazel
TI - Hereditary circuit spaces
JO - Compositio Mathematica
PY - 1978
PB - Sijthoff et Noordhoff International Publishers
VL - 37
IS - 3
SP - 339
EP - 351
LA - eng
KW - Circuit Spaces; Independence Spaces Matroids
UR - http://eudml.org/doc/89387
ER -

References

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  1. [1] G. Birkhoff: Combinatorial relations in projective geometries. Ann. Math., 36 (1935) 743-748. Zbl0012.08205MR1503250JFM61.0593.01
  2. [2] G. Birkhoff: Lattice Theory (3rd Ed.). American Mathematical Society Colloquium Publications, 1967. Zbl0505.06001MR227053
  3. [3] V.W. Bryant and J.E. Dawson: Designs and circuit bases. Archiv der Math. (to appear). Zbl0373.05022MR505592
  4. [4] V.W. Bryant and H. Perfect: Some characterization theorems for circuit spaces associated with graphs. Discrete Math;18 (1977) 109-124. Zbl0355.05016MR465943
  5. [5] H.H. Crapo and G.-C. Rota: Combinatorial Geometries. M.I.T. Press, 1970. Zbl0231.05024MR290980
  6. [6] J.E. Dawson: Balanced sets and circuits in a transversal space. J. Comb. Theory Ser. B;23 (1977) 14-23. Zbl0369.05018MR453569
  7. [7] H. Hadwiger, H.E. Debrunner and V. Klee: Combinatorial Geometry in the Plane. Holt, Rinehart and Winston, 1964. MR164279
  8. [8] A.W. Ingleton and M.J. Piff: Gammoids and transversal matroids. J. Comb, Theory, 15 (1973) 51-68. Zbl0264.05021MR329936
  9. [9] F. Maeda and S. Maeda: Theory of Symmetric Lattices. Springer-Verlag, 1970. Zbl0219.06002MR282889
  10. [10] L. Mirsky: Transversal Theory. Academic Press, 1971. Zbl0282.05001MR282853
  11. [11] Th. Motzkin: The lines and planes connecting the points of a finite set. Trans. Amer. Math. Soc., 70 (1951) 451-464. Zbl0043.14603MR41447
  12. [12] U.S.R. Murty: Sylvester matroids. Recent progress in Combinatorics, Wiley, 1969, 283-286. Zbl0196.02701MR255432
  13. [13] U.S.R. Murty: Matroids with Sylvester property. Aequat. Math., 4 (1970) 44-50. Zbl0216.30203MR265186
  14. [14] H. Perfect: Notes on circuit spaces: J. Math. Anal. & Applic., 54 (1976) 530-537. Zbl0335.05032MR427111
  15. [15] M.J. Piff and D.J.A. Welsh: On the vector representation of matroids. J. London Math. Soc., (2)2 (1970) 284-288. Zbl0213.29102MR258662
  16. [16] D.E. Rutherford: Introduction to Lattice Theory, Oliver and Boyd. 1965. Zbl0127.24904MR176942
  17. [17] P. Vámos: On the representation of independence structures. (Unpublished). 
  18. [18] P. Vámos: The importance of finiteness of Sylvester matroids. (Not yet published). 
  19. [19] D.J.A. Welsh: Matroid Theory. Academic Press, 1976. Zbl0343.05002MR427112

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