Existence theorems for matroid designs

Young, H. Peyton

doi:10.1090/S0002-9947-1973-0406834-X

Existence theorems for matroid designs
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Trans. Amer. Math. Soc. 183 (1973), 1-35 Request permission

Abstract:

A study is made of matroids in which the hyperplanes have equal cardinality. Fundamental constructions of such matroids are exhibited, and existence theorems are proved for large parametric classes of them.

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Über Steinersche Systeme

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Peyton Young, U. S. R. Murty, and Jack Edmonds, Equicardinal matroids and matroid-designs, Proc. Second Chapel Hill Conf. on Combinatorial Mathematics and its Applications (Univ. North Carolina, Chapel Hill, N.C., 1970) Univ. North Carolina, Chapel Hill, N.C., 1970, pp. 498–542. MR 0266782
Peyton Young and Jack Edmonds, Matroid designs, J. Res. Nat. Bur. Standards Sect. B 77B (1973), 15–44. MR 382041, DOI 10.6028/jres.077B.003