# Permanents and determinants of (0,1) matrices

Meeussen Wouter (bkarnd) wouter.meeussen at vandemoortele.com
Fri Oct 31 18:18:14 CET 2003

```permanents: n=1..4
{2, 3, 6, 16}

{
{{0, 1}, {1, 1}},
{{0, 9}, {1, 6}, {2, 1}},
{{0, 265}, {1, 150}, {2, 69}, {3, 18}, {4, 9}, {6, 1}},
{{0, 27713}, {1, 13032}, {2, 10800},
{3, 4992}, {4, 4254}, {5, 1440}, {6, 1536}, {7, 576}, {8, 648}, {9,
24}, {10, 288}, {11, 96}, {12, 48}, {14, 72}, {18, 16}, {24, 1}}
}
Determinants: n=1..4
{2, 3, 5, 7}

{
{{0, 1}, {1, 1}},
{{-1, 3}, {0, 10}, {1, 3}},
{{-2, 3}, {-1, 84}, {0, 338}, {1, 84}, {2, 3}},
{{-3, 60}, {-2, 1200}, {-1, 10020}, {0,
42976}, {1, 10020}, {2, 1200}, {3, 60}}
}
{{Det=-1, 3 times}, {Det=0, 10 times}, {Det=1, 3 times}}
3+10+3= 16 cases in all= 2^(2^2)

is that what you asked for?

W.

a propos,
no comments yet on on row- and column sorting of binary matrices;
so I refrain from submitting, fearing oversight of somthin' obvious.

-----Original Message-----
From: Yuval Dekel [mailto:dekelyuval at hotmail.com]
Sent: vrijdag 31 oktober 2003 17:37
To: seqfan at ext.jussieu.fr
Subject: Permanents and determinants of (0,1) matrices

Following sequence A087983 let :

a(n) = number of different values taken by permanents of nonsingular nxn
(0,1) matrices ,
b(n) = number of different values taken by determinants of nxn (0,1)
matrices .

Can someone comupte a(n) and b(n) ?

Thanks,
Yuval

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