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The aim of this paper is to give a new combinatorial proof of Fisher’s inequality and to prove that if t is odd, t>1, ε>0 and b is the number of blocks of a t−(v,k,λ) design, then b≧(1−ε)(λ2t−(λ−1)2t)t2(t−1)−t2vt2 for v≧v0.
The Legendre–Stirling numbers are the coefficients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejohn gave...
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