Lower bounds for permanents of incidence matrices

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Abstract

If A is the incidence matrix of a vkλ configuration with λ > 1, it is shown that perA−|detA|⩽λ(λ−1)(k−2)!(k−q)! where q is the least integer greater than or equal to 12λkkλ(k+λ) If A is the incidence matrix of a projective plane of order m ⩾ 3, it is shown that perA−|detA|⩽(m+1)2(m+1)!(m−q+5)! where q is the least integer greater than or equal to m2+4m+1+1 It is an immediate corollary that per A > | det A | for all vkλ configurations except the 7 − 3 − 1 and 3 − 2 − 1 configurations.

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Present address: Florida Atlantic University, Boca Raton, Florida 33432.