In this paper we are concerned with the following conjecture. Conjecture: Let L be a collection of k positive integers and In particular, we show this conjecture is true when L consists of k consecutive positive integers. This generalizes a well-known inequality of Fisher's. Our proof simplifies an
Fisher's inequality revisited
β Scribed by Takashi Hara; Hal Tasaki
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 165 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0375-9601
No coin nor oath required. For personal study only.
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A new proof is given of the nonuniform version of Fisher's inequality, first proved by Majumdar. The proof is ``elementary,'' in the sense of being purely combinatorial and not using ideas from linear algebra. However, no nonalgebraic proof of the n-dimensional analogue of this result (Theorem 3 her
on v points and b lines the number of intersecting line-pairs is at least (z). This clearly implies b 2 v.
Nous donnons ici une dtmonstration nouvelle, trts courte, de I'iGgaliti de Fisher, qui gCntralise un rCsultat bien connu de de Bruijn et ErdGs. Cette dtmonstration utilise essentiellement une id&e de Tverberg (1982) pour dt-montrer un autre tnonct combinatoire. We prove the following result.
tn this paper we study subsets of 8 finite set that intersect each other in at most one eleml~ont, Etch subaet intersects mogt of the other subsets in exwtly one element. The Mowing theorem is one of our main conduaions, tot S,, 1 . . , S,,, be m subrreta ot' an n=aet S with IS,1 22 (1~ I, 1.1, tti)