Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 122.24802
Autor: Erdös, Pál; Hanani, H.
Title: On a limit theorem in combinatorial analysis (In English)
Source: Publ. Math. 10, 10-13 (1964).
Review: Let M(k,l,n)(m(k,l,n)) be a minimal (maximal) system of combinations of k out of n such that every combination of l occurs at least (at most) once. Let | M(k,l,n) | (| m(k,l,n) |) be the number of combinations in M(k,l,n) (m(k,l,n)) and \mu(k,l,n) = | M(k,l,n) | {{k \choose l}\over {n \choose l}}, \nu(k,l,n) = | m(k,l,n) | {{k \choose l} \over {n \choose l}}. Trivially \nu (k,l,n) \leq 1 \leq \mu (k,l,n). The authors prove limn ––> oo \mu(k,2,n) = limn ––> oo\nu (k,2,n) = 1. If p is a power of a prime then limn ––> oo\mu (p+1,3,n) = limn ––> oo \nu (p+1,3,n) = 1.
Reviewer: H.B.Mann
Classif.: * 05A05 Combinatorial choice problems
05A15 Combinatorial enumeration problems
Index Words: combinatorics
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