Permanents and determinants of (0,1) matrices
Jaap Spies
j.spies at hccnet.nl
Wed Nov 12 00:30:52 CET 2003
N. J. A. Sloane wrote:
> Hugo asked which of those sequences should be submitted. Well, let's see:
>
[...]
>
> Maximal permanent of a real non-singular (0,1)-matrix of order n:
> 1 1 3 11 53
next value 309
> Number of real non-singular (0,1)-matrices having maximal permanent=
> a(from previous sequence)
> 1 6 18 96 600
next value 4320
>
> Number of different values that can be assumed by the
> permanent of a real non-singular (0,1)-matrix of order n:
> 1 1 3 9 31 (will Jaap Spies compute a(6)?)
>
a(6)= 149
I send the raw data I got after almost 5 days stupid brute force processing
of 2^36 (0,1)-matrices.
Still studying on the smart approach of Gordon!
Edwin, I did not check the total! ;-)
Jaap
permanent
frequency
1, 2722666320
2, 794905920
3, 3177482112
4, 940377600
5, 2396752416
6, 1003410720
7, 2065396896
8, 797018400
9, 1468176624
10, 757728000
11, 1350274464
12, 577540800
13, 1033903872
14, 611107200
15, 829554336
16, 401846400
17, 769815072
18, 392947200
19, 535726848
20, 371239200
21, 569427840
22, 263952000
23, 375026976
24, 235612800
25, 440866368
26, 209692800
27, 260427168
28, 160790400
29, 288715680
30, 152755200
31, 262855872
32, 135302400
33, 173964528
34, 118627200
35, 176914368
36, 89553600
37, 134433408
38, 83721600
39, 156507840
40, 68817600
41, 100016928
42, 75859200
43, 97309728
44, 59672160
45, 86154048
46, 49766400
47, 74633184
48, 28166400
49, 64561248
50, 34084800
51, 56572992
52, 40694400
53, 66711456
54, 32270400
55, 42234048
56, 23846400
57, 35541792
58, 16070400
59, 32389920
60, 15811200
61, 34138368
62, 10821600
63, 31490880
64, 22809600
65, 21494592
66, 12268800
67, 25658784
68, 14169600
69, 18141696
70, 12960000
71, 20814336
72, 7257600
73, 11055168
74, 3628800
75, 18832128
76, 5184000
77, 11835456
78, 6220800
79, 9063936
80, 2592000
81, 12247200
82, 4413600
83, 11404800
84, 5486400
85, 8812800
86, 3974400
87, 5184000
88, 3110400
89, 8419968
90, 2592000
91, 4664448
92, 3628800
93, 5313600
94, 518400
95, 3849408
96, 2073600
97, 5961600
98, 777600
99, 4665600
100, 777600
101, 2587968
102, 1555200
103, 4658688
105, 1555200
106, 1382400
107, 3628800
108, 570240
109, 2462400
110, 2160000
111, 2073600
112, 604800
113, 518400
114, 518400
115, 2160000
116, 518400
117, 2332800
120, 777600
121, 2073600
123, 1036800
125, 1810944
127, 1036800
128, 432000
129, 1036800
130, 86400
131, 1814400
134, 518400
135, 1036800
137, 532800
139, 259200
141, 648000
142, 86400
145, 518400
149, 1036800
150, 86400
153, 1036800
156, 43200
159, 604800
161, 518400
167, 518400
170, 86400
173, 129600
181, 259200
195, 259200
199, 259200
203, 86400
212, 21600
245, 86400
265, 720
309, 4320
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