A Fisher type inequality
β Scribed by D.E. Keenan
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 318 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
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) and IS,nS#4 (1~1; 1, f4,a.r, m), Suppose further th;tt for Borne flxsd positive integer c each S, hcrtr non=smpty interaectian with trt le~lst m -c( of the femtiining subeta, Thctr
π SIMILAR VOLUMES
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
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.