Geodesic
On the Permanent of a Certain Class of (0, 1)-Matrices
Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 507-511

Voir la notice de l'article provenant de la source Cambridge University Press

In [3, p. 77] Ryser notes the importance of the minimum of the permanent function on the class of (0, 1)-matrices having exactly k ones in each row and column. In [4] a lower bound was found for the minimum of the permanent on the class Λn of n × n (0, 1)-matrices with exactly three l's in each row and column. The purpose of our work is to improve this result, in particular we show that minA ∊ Λn (per A) ≥ 3(n-1). 
Hartfiel, D. J.; Crosby, J. W. On the Permanent of a Certain Class of (0, 1)-Matrices. Canadian mathematical bulletin, Tome 14 (1971) no. 4, pp. 507-511. doi: 10.4153/CMB-1971-091-1
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[1] 1. Hartfiel, D. J., A simplified form for nearly reducible and nearly decomposable matrices, Proc. Amer. Math. Soc. 24 (1970), 388-393. Google Scholar

[2] 2. Mine, H., On lower bounds for permanents of (0, 1) matrices, Proc. Amer. Math. Soc. 22 (1969), 117-123. Google Scholar

[3] 3. Ryser, H. J., Combinatorial mathematics, Carus Monograph No. 14, Amer. Math. Soc. 1963. Google Scholar

[4] 4. Sinkhorn, R., Concerning a conjecture of Marshall Hall, Proc. Amer. Math. Soc. 21 (1969), 197-201. Google Scholar

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