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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 herein) seems to be known. ## 1997 Academic Press A design D consists of a family B 1 , ..., B b of subets, called blocks, of a finite set S=[P 1 , ..., P v ] whose elements are called points or varieties. D is balanced or \*-linked if every pair of points is contained in exactly \* blocks. If, in addition, \*>0 and no block contains all the points, then D is nontrivial, and if every block has the same cardinality k then D is a balanced incomplete-block design or BIBD. Fisher [5] proved that if D is a BIBD, then b v. Bose [3] gave a neat short proof of this result using a determinant. Majumdar [8] provided an easy modification of Bose's method that extends the result to arbitrary non-trivial \*-linked designs, which one can think of as a nonuniform version of Fisher's inequality. (The case \*=1 of Majumdar's result had been proved earlier by de Bruijn and Erdo s [4].) My attention has recen

Who reads A Note on Fisher's Inequality?

Author

Douglas R. Woodall

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0097-3165)

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)