A087983
Number of different values taken by permanent of n X n (0,1)-matrix.
Original entry on oeis.org
1, 2, 3, 6, 16, 51, 220, 1179, 7980
Offset: 0
For a 4 X 4 matrix the 16 possible permanents and their multiplicieties are:
{{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}}
A089479
Triangle T(n,k) read by rows, where T(n,k) = number of times the permanent of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= n!.
Original entry on oeis.org
0, 1, 1, 1, 9, 6, 1, 265, 150, 69, 18, 9, 0, 1, 27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288, 96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1, 10363361, 3513720, 4339440, 2626800, 3015450, 1451400, 1872800, 962400, 1295700, 425400, 873000
Offset: 0
Triangle begins:
0, 1;
1, 1;
9, 6, 1;
265, 150, 69, 18, 9, 0, 1;
27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288,
96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1;
...
T(n,0) =
A088672(n), T(n,1) =
A089482(n). The n-th row of the table contains
A087983(n) nonzero entries. For n>2
A089477(n) gives the position of the first zero entry in the n-th row.
Cf.
A089480 (occurrence counts for permanents of non-singular (0,1)-matrices),
A089481 (occurrence counts for permanents of singular (0,1)-matrices).
A192892
Number of n X n binary matrices whose determinants equal their permanents.
Original entry on oeis.org
1, 2, 12, 343, 34997, 12515441, 15749457081, 72424550598849, 1282759836215548737
Offset: 0
a(2) equals 12 because there are exactly twelve 2 X 2 binary matrices whose determinants equal their permanents; these matrices are:
|0 0| |1 0| |0 1| |1 1| |0 0| |1 0| |0 0| |1 0|
|0 0| |0 0| |0 0| |0 0| |1 0| |1 0| |0 1| |0 1|
.
|0 1| |1 1| |0 0| |1 0|
|0 1| |0 1| |1 1| |1 1|
-
Sum[KroneckerDelta[Det[Array[Mod[Floor[k/(2^(n*(#1 - 1) + #2 - 1))], 2] &, {n, n}]], Permanent[Array[Mod[Floor[k/(2^(n*(#1 - 1) + #2 - 1))], 2] &, {n, n}]]], {k, 0, (2^(n^2)) - 1}]
-
from itertools import product
from sympy import Matrix
def A192892(n): return 1 if n == 0 else sum(1 for m in product([0,1],repeat=n**2) if (lambda x:x.det()==x.per())(Matrix(n,n,m))) # Chai Wah Wu, Oct 01 2021
Definition and example slightly modified by
Harvey P. Dale, Feb 24 2017
A081473
Smallest positive even number not the permanent of a real singular (0,1)-matrix of order n.
Original entry on oeis.org
2, 4, 8, 16, 44, 194, 946
Offset: 1
a(4) = 16, see permanent frequency table: (0,27713), (2,9360), (4,3582), (6,1248), (8,648), (10,288), (12,48), (14,72), (18,16), (24,1).
Showing 1-4 of 4 results.
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