# Permanents and determinants of (0,1) matrices

Jaap Spies j.spies at hccnet.nl
Sun Nov 2 02:13:11 CET 2003

```Jaap Spies wrote:
> Yuval Dekel wrote:
>
>> 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
>>

> a(1)=1, a(2)=1, a(3)=3, a(4)=9, a(5)=33, ...,

>
> Example: the permanent of a 4*4 nonsingular (0,1) matrix
> can have values 1,2,3,4,5,6,7,9,11
>
> Jaap Spies
>
> .
>
I have to correct myself. Thanks to Edwin Clark, who pointed out
that my frequencies do not add up to the results of A055165
ID Number: A055165
URL:       http://www.research.att.com/projects/OEIS?Anum=A055165
Sequence:  1,6,174,22560,12514320,28836612000,270345669985440

Here are my new results

n=1
{1, 1}
n=2
{1, 6}
n=3
{1, 150}, {2, 6}, {3, 18}
n=4
{1, 13032}, {2, 1440}, {3, 4992}, {4, 672}, {5, 1440}, {6, 288}, {7, 576}
{9, 24}, {11, 96}
n=5
{1, 3513720}, {2, 693840}, {3, 2626800}, {4, 604200}, {5, 1451400}, {6, 468000}
{7, 962400}, {8, 252000}, {9, 425400}, {10, 190800}, {11, 379200}, {12, 97200}
{13, 205440}, {14, 100800}, {15, 132000}, {16, 28800}, {17, 108000}, {18, 28800}
{19, 44400}, {20, 33600}, {21, 61200}, {22, 9600}, {23, 14400}, {25, 36000}
{26, 7200}, {29, 14400}, {31, 14400}, {33, 2400}, {39, 7200}, {44, 120}, {53, 600}

So a(1)=1, a(2)=1, a(3)=3, a(4)=9, a(5)=31, ...,

a(6) is hard to get.

Jaap Spies

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