A catalogue of combinatorial geometries

Authors:
John E. Blackburn, Henry H. Crapo and Denis A. Higgs

Journal:
Math. Comp. **27** (1973), 155-166

MSC:
Primary 05B35

DOI:
https://doi.org/10.1090/S0025-5718-1973-0419270-0

MathSciNet review:
0419270

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We include in the microfiche section of this issue a catalogue of all the different geometric configurations which may be constructed from *n* points, , by specifying their points, lines, planes, . . . , colines, copoints, their *flats* of each rank. It suffices to list the copoints of each combinatorial geometry *G*, because the colines of *G* are the copoints of a geometry earlier in the list, which may be located by deleting one component of the designator of *G*.

**[1]**H. H. Crapo, "Single-element extensions of matroids,"*J. Res. Nat. Bur. Standards Sect. B*, v. 69B, 1965, pp. 55-65. MR**32**#7461. MR**0190045 (32:7461)****[2]**H. H. Crapo & G.-C. Rota,*On the Foundations of Combinational Theory*:*Combinatorial Geometries*, M.I.T. Press, Cambridge, Mass., 1970. (Preliminary edition.) MR**0290980 (45:74)****[3]**H. H. Crapo, "The Tutte polynomial,"*Aequationes Math.*, v. 3, 1969, pp. 211-229. MR**41**#6705. MR**0262095 (41:6705)****[4]**J. Doyen, "Sur le nombre d'espaces linéaires non isomorphes de*n*points,"*Bull. Soc. Math. Belg.*, v. 19, 1967, pp. 421-437. MR**40**#2562. MR**0249316 (40:2562)****[5]**D. A. Higgs, "Matroids on 6, 7 elements," 1966. (Unpublished.)**[6]**A. W. Ingleton, "A note on independence functions and rank,"*J. London Math. Soc.*, v. 34, 1959, pp. 49-56. MR**21**#655. MR**0101848 (21:655)****[7]**A. W. Ingleton, "Representation of matroids,"*Combinatorial Mathematics and Its Applications*(Proc. Conf., Oxford, 1969), Academic Press, London, 1971, pp. 149-167. MR**43**#4700. MR**0278974 (43:4700)****[8]**M. J. Piff & D. J. A. Welsh,*On the Number of Combinatorial Geometries*, Mathematical Institute, University of Oxford, 1971. (Preprint.) MR**0282867 (44:101)****[9]**D. J. A. Welsh, "A bound for the number of matroids,"*J. Combinatorial Theory*, v. 6, 1969, pp. 313-316. MR**39**#87. MR**0238723 (39:87)**

Retrieve articles in *Mathematics of Computation*
with MSC:
05B35

Retrieve articles in all journals with MSC: 05B35

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0419270-0

Keywords:
Combinatorial geometries,
geometric lattice,
configuration,
catalogue of geometries,
modular filter,
Tutte polynomial

Article copyright:
© Copyright 1973
American Mathematical Society