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article · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · 1973

Matroid designs

P. Young, J. Edmonds

Cited by 9Open access

Abstract

Matroids are investigated in which equicardinality conditions are imposed on the flats. S uch matroids are shown to be closely related to ce rt ain types of BIB D's . Ex iste nce and unique ness theorems for thes e structures are derive d, toge th er with a bound ed ness crit eri on on th eir rank. Several classes are exhibited , in cludin g finite proj ective and affine geo metri es, ce rt ain tdesigns (S tein er sys te ms) and so-called trivi oid s. By vi e win g ce rtain t -des igns as matroids, new ways of constructin g BIBD's are deriv ed. Three ne w seri es of 3designs a nd two new 4designs are obtained by th ese methods. A matroid analysis of th e 5(24,8,1) desi gn of Witt is prese nte d, and exam pl es are obtained from it of matroids havin g e qui cardin al hyperpl anes but not e qui cardin a l fl ats in lower rank s. Several ge neral co nj ectures a nd exi ste nce prob lems for these t ypes of matroids are sugges ted.

Cite this paper

APA 7

Young, P., & Edmonds, J. (1973). Matroid designs. Journal of Research of the National Bureau of Standards Section B Mathematical Sciences, 77B(1 and 2), 15. https://doi.org/10.6028/jres.077b.003

MLA 9

Young, P., and J. Edmonds. “Matroid designs.” Journal of Research of the National Bureau of Standards Section B Mathematical Sciences, vol. 77B, no. 1 and 2, 1973, p. 15, https://doi.org/10.6028/jres.077b.003.

Chicago

Young, P., and J. Edmonds. 1973. “Matroid designs.” Journal of Research of the National Bureau of Standards Section B Mathematical Sciences 77B (1 and 2): 15. https://doi.org/10.6028/jres.077b.003.

Harvard

Young, P. and Edmonds, J. (1973) ‘Matroid designs’, Journal of Research of the National Bureau of Standards Section B Mathematical Sciences, 77B(1 and 2), p. 15. Available at: https://doi.org/10.6028/jres.077b.003.

BibTeX
@article{young1973matroid,
  title = {{Matroid designs}},
  author = {Young, P. and Edmonds, J.},
  journal = {Journal of Research of the National Bureau of Standards Section B Mathematical Sciences},
  volume = {77B},
  number = {1 and 2},
  pages = {15},
  year = {1973},
  doi = {10.6028/jres.077b.003}
}

Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.

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