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
A Generalization of Fisher's Inequality
β Scribed by Hunter S. Snevily
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 97 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0097-3165
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β¦ Synopsis
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 and extends a recent result of Ramanan's.
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