Vol. 95, No. 1, 1981

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Concerning the minimum of permanents on doubly stochastic circulants

Gerald Suchan

Vol. 95 (1981), No. 1, 213–217
Abstract

Let Pn be the permutation matrix such that (Pn)ij = 1 if j = i + 1 (mod n). Mine [2] proved that the minimum of the permanent on the collection of n × n doubly stochastic circulants αIn + βPn + γPn2 is in (12n,12n1], and if n 5 then the minimum is not achieved at (13)In + (13)Pn + (13)Pn2. This paper proves that if n 3 then the minimum of such permanents is less than 12n1, and if n ∈{3,4} then this minimum is uniquely achieved at (13)In + (13)Pn + (13)Pn2.

Mathematical Subject Classification 2000
Primary: 15A15
Milestones
Received: 3 July 1973
Published: 1 July 1981
Authors
Gerald Suchan