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Variations on a theorem of Ryser

✍ Scribed by Dasong Cao; V. Chvátal; A.J. Hoffman; A. Vince

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
304 KB
Volume
260
Category
Article
ISSN
0024-3795

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✦ Synopsis

A famous theorem of Ryser asserts that a v x v zero-one matrix A satisfying AA r --(k -k)I + aJ with k ~ k must satisfy k + (v -1)k = k 2 and ArA (k -k)I + A J; such a matrix A is called the incidence matrix of a symmetric block design. We present a new, e/ementary proof of Ryser's theorem and give a characterization of the incidence matrices of symmetric block designs that involves eigenvalues of AA r.

📜 SIMILAR VOLUMES

A generalization of Ryser's theorem on t
A generalization of Ryser's theorem on term rank
✍ Kevin McDougal 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 233 KB

In his work on classes of (0, 1 )-matrices with given row and column sum vectors, Herbert Ryser proved that the maximum term rank possible in a normalized class, p, can be realized by a matrix having p (independent) l's in positions (1,p),(2,p-1) ..... (p, 1). We study the positions occupied by sets