Statistics

Matroids and characteristic set classes by bucket

rank	n	matroids	cofinite	finite	empty	unknown
2	2	1	—	—	—	—
2	3	3	—	—	—	—
2	4	7	—	—	—	—
2	5	13	—	—	—	—
2	6	23	—	—	—	—
2	7	37	—	—	—	—
2	8	58	—	—	—	—
3	3	1	1	0	0	0
3	4	4	4	0	0	0
3	5	13	13	0	0	0
3	6	38	38	0	0	0
3	7	108	107	1	0	0
3	8	325	321	4	0	0
3	9	1,275	1,251	20	4	0
3	10	10,037	9,725	142	170	0
3	11	298,491	280,446	2,725	15,320	0
3	12	31,899,134	27,448,979	334,798	3,844,731	270,626
4	4	1	1	0	0	0
4	5	5	5	0	0	0
4	6	23	23	0	0	0
4	7	108	107	1	0	0
4	8	940	876	20	44	0
4	9	190,214	150,244	1,980	37,990	0

Realization space dimension

rs_dim	matroids
-1	4,237,950
0	2,017,782
1	5,700,971
2	8,037,716
3	6,657,451
4	3,621,120
5	1,370,644
6	381,879
7	84,160
8	16,388
9	3,131
10	676
11	154
12	49
13	12
14	6
15	1
16	1
unknown	270,626

Birational types

birational type	matroids
rational	419,842
empty	58,421
rational over Q(a)/(a^2 - a + 1)	2,480
point over Q(a)/(a^3 - a^2 + 1)	1,861
genus 1 curve (11a3)	1,855
point over Q(a)/(a^2 - a - 1)	1,643
point over Q(a)/(a^2 - a + 1)	1,579
point over Q(a)/(a^2 + 1)	1,469
point over Q(a)/(a^2 - 2)	1,178
rational over Q(a)/(a^2 - a - 1)	1,036
K3 surface	992
genus 1 curve (14a4)	904
genus 1 curve (15a8)	649
point over Q(a)/(a^2 - a + 2)	608
rational over Q(a)/(a^2 + 1)	599
curve of genus 2	576
point over Q(a)/(a^3 + a - 1)	566
genus 1 curve (37a1)	557
point over Q(a)/(a^3 - a^2 + a + 1)	521
point over Q(a)/(a^3 - a^2 - 2*a + 1)	350
point over Q(a)/(a^4 - a^3 - a^2 + a + 1)	298
genus 1 curve (17a4)	204
rational over Q(a)/(a^3 - a^2 + 1)	199
point over Q(a)/(a^2 - 3)	187
genus 1 curve (43a1)	186
point over Q(a)/(a^4 - a - 1)	178
genus 1 curve (20a2)	167
genus 1 curve (11a3) x P^1	165
point over Q(a)/(a^2 - a - 4)	141
genus 1 curve (53a1)	123
point over Q(a)/(a^4 - a^3 + a^2 - a + 1)	115
genus 1 curve (19a3)	108
rational over Q(a)/(a^2 - 2)	98
point over Q(a)/(a^4 - a^3 + 2*a - 1)	94
genus 1 curve (58a1)	92
point over Q(a)/(a^3 + 2*a - 1)	77
point over Q(a)/(a^2 + 2)	75
point over Q(a)/(a^4 + a^2 - a + 1)	69
point over Q(a)/(a^4 - a^3 + a^2 + a - 1)	66
point over Q(a)/(a^4 - a^2 + 1)	49
genus 1 curve (65a1)	48
curve of genus 3	47
point over Q(a)/(a^3 - a - 2)	44
K3 surface x P^1	44
genus 1 curve (14a4) x P^1	40
genus 1 curve (24a4)	37
point over Q(a)/(a^4 - a^3 + 2*a + 1)	36
point over Q(a)/(a^3 - 2*a - 2)	35
point over Q(a)/(a^3 - 3*a - 1)	34
Calabi-Yau threefold (elliptic over P^1 x P^1, K trivial; kappa = 0, not rational)	33
point over Q(a)/(a^5 - a^3 - a^2 + a + 1)	32
genus 1 curve (27a3)	31
genus 1 curve (15a8) x P^1	30
ruled over the genus 1 curve 11a3	26
rational over Q(a)/(a^2 - a + 2)	25
genus 1 curve	25
point over Q(a)/(a^5 - a^4 + a^2 - a + 1)	24
genus 1 curve (37a1) x P^1	23
point over Q(a)/(a^4 + 1)	22
rational over Q(a)/(a^3 - a^2 + a + 1)	22
genus 1 curve (61a1)	22
point over Q(a)/(a^5 - a^4 + a^3 - 2*a^2 + a - 1)	21
point over Q(a)/(a^4 - a + 1)	19
point over Q(a)/(a^3 - a^2 - 2)	19
genus 1 curve (21a4)	19
genus 1 curve (57a1)	16
point over Q(a)/(a^3 - a^2 - 3*a + 1)	15
point over Q(a)/(a^4 - a^3 - a^2 + 3*a - 1)	14
point over Q(a)/(a^4 - 2*a^3 + 2)	13
point over Q(a)/(a^4 - 2*a - 1)	13
point over Q(a)/(a^2 - a - 3)	13
point over Q(a)/(a^4 - a^3 - a^2 - a + 1)	11
genus 1 curve (92b1)	10
genus 1 curve (32a2)	10
point over Q(a)/(a^2 - a + 4)	10
genus 1 curve (34a1)	10
rational over Q(a)/(a^3 - a^2 - 2*a + 1)	10
point over Q(a)/(a^4 - a^3 + a^2 - a - 1)	9
genus 1 curve (26b1)	9
point over Q(a)/(a^4 - a^3 - 3*a^2 + a + 1)	8
rational over Q(a)/(a^4 - a^3 + a^2 - a + 1)	8
point over Q(a)/(a^5 - 2a^4 + 2a^3 - a^2 + 1)	7
genus 1 curve (79a1)	7
ruled over the genus 1 curve 15a8	7
point over Q(a)/(a^4 - a^3 + a + 1)	6
point over Q(a)/(a^4 - 2a^3 + a^2 - 2a + 1)	6
genus 1 curve (101a1)	6
genus 1 curve (89a1)	6
genus 1 curve (38b1)	6
genus 1 curve (82a1)	6
point over Q(a)/(a^4 - 2*a^3 + a^2 - a - 1)	6
point over Q(a)/(a^2 - a - 8)	6
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(0,-1) - 0E (rationality undetermined)	6
genus 1 curve (11a3) x P^2	6
point over Q(a)/(a^5 - a^3 - 2*a^2 + 1)	5
genus 1 curve (36a1)	5
point over Q(a)/(a^3 - 2)	5
point over Q(a)/(a^4 - a^2 - 1)	5
point over Q(a)/(a^3 - a^2 + a - 2)	5
point over Q(a)/(a^3 - a^2 - 2*a - 2)	5
genus 1 curve (83a1)	5
genus 1 curve (26a3)	5
genus 1 curve (24a1)	4
genus 1 curve (102a1)	4
genus 1 curve (124a1)	4
point over Q(a)/(a^3 - a^2 + 2*a + 1)	4
point over Q(a)/(a^5 - a^4 + a^3 - a^2 - 1)	4
genus 1 curve (39a4)	4
K3 surface x P^2	4
genus 1 curve (35a3)	4
point over Q(a)/(a^5 + a^3 - 2*a^2 - 1)	3
genus 1 curve (99a1)	3
point over Q(a)/(a^5 - a^4 + a^3 - a^2 + 2*a - 1)	3
point over Q(a)/(a^4 + 2a^2 - 2a + 1)	3
genus 1 curve (62a1)	3
ruled over the genus 1 curve 14a4	3
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(-1,-1) - 0E (rationality undetermined)	3
curve of genus 4	3
point over Q(a)/(a^6 - a^5 - a^2 + a + 1)	3
genus 1 curve (131a1)	3
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(0,0) - 1E (rationality undetermined)	2
genus 1 curve (155c1)	2
point over Q(a)/(a^5 - a^4 - a^3 + 3*a^2 - 1)	2
point over Q(a)/(a^5 + 2a^3 - a^2 + 2a - 1)	2
genus 1 curve (40a3)	2
genus 1 curve (14a4) x P^2	2
point over Q(a)/(a^5 - a^4 - a^3 + 2*a^2 - a - 1)	2
point over Q(a)/(a^4 - 2*a^2 - 1)	2
genus 1 curve (42a1)	2
point over Q(a)/(a^4 - a^3 + 2a^2 - 2a + 2)	2
point over Q(a)/(a^3 - a^2 - 4*a + 2)	2
point over Q(a)/(a^2 - 7)	2
genus 1 curve (15a8) x P^2	2
point over Q(a)/(a^6 - a^5 + 2a^4 - 2a^3 + 2a^2 - 2a + 1)	2
point over Q(a)/(a^5 - 2a^2 - 2a - 1)	1
point over Q(a)/(a^5 + a^3 - 2*a^2 - a - 1)	1
point over Q(a)/(a^6 + 2a^4 - a^3 + 2a^2 + 1)	1
genus 1 curve (55a4)	1
genus 1 curve (141d1)	1
genus 1 curve (48a4)	1
point over Q(a)/(a^6 - 2a^4 - a^3 + 2a + 1)	1
point over Q(a)/(a^6 - a^5 + a^4 + 2a^3 - 4a^2 + 3*a - 1)	1
point over Q(a)/(a^6 - a^5 + a^4 - 2*a^2 + a - 1)	1
point over Q(a)/(a^6 - a^5 - a^4 + 2*a^3 - a + 1)	1
genus 1 curve (37a1) x P^2	1
ruled over the genus 1 curve 37a1	1
genus 1 curve (91b1)	1
point over Q(a)/(a^6 - a^5 - a - 1)	1
point over Q(a)/(a^4 - 2a^3 - 2a + 1)	1
point over Q(a)/(a^6 - a^5 + 4a^3 - 2a^2 - 2*a + 1)	1
point over Q(a)/(a^5 - a^4 + 2*a^2 - a + 1)	1
point over Q(a)/(a^4 - a^3 - 2*a^2 + 3)	1
genus 1 curve (389a1)	1
genus 1 curve (196a1)	1
genus 1 curve (118a1)	1
point over Q(a)/(a^6 - a^5 + 2a^4 - 3a^3 + 2*a^2 - a + 1)	1
point over Q(a)/(a^5 - a^4 - 4a^2 + 3a + 2)	1
point over Q(a)/(a^5 - a^2 - 1)	1
point over Q(a)/(a^5 - a^4 - a^3 + 2*a + 1)	1
point over Q(a)/(a^4 - a^3 - 2*a^2 - a + 1)	1
point over Q(a)/(a^5 - a^4 + a + 1)	1
point over Q(a)/(a^4 - 2a^3 + 5a^2 - 4*a + 2)	1
point over Q(a)/(a^5 - 2*a^2 - 1)	1
point over Q(a)/(a^4 - a^2 - 3*a - 1)	1
point over Q(a)/(a^5 - 2a^4 + 2a^3 - 2*a + 2)	1
point over Q(a)/(a^4 - 2*a^3 + a^2 - 2)	1
point over Q(a)/(a^3 - a^2 + a - 3)	1
genus 1 curve (158a1)	1
point over Q(a)/(a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)	1
point over Q(a)/(a^4 - a^3 + 2*a^2 - a + 2)	1
point over Q(a)/(a^5 + a^3 + a - 1)	1
genus 1 curve (15a3)	1
point over Q(a)/(a^5 - 2a^4 + 2a^3 - 2*a^2 - 1)	1
point over Q(a)/(a^5 - a^4 + 2*a^3 - a^2 + 1)	1
point over Q(a)/(a^5 - a^4 + 2a^3 - a^2 + 2a - 1)	1
genus 1 curve (433a1)	1
point over Q(a)/(a^5 - 2a^4 + a^3 + 2a^2 - 2*a - 1)	1
point over Q(a)/(a^4 - 2a^3 - a^2 + 2a + 2)	1
point over Q(a)/(a^4 - 4*a^2 + 1)	1
point over Q(a)/(a^3 - a^2 - 4*a - 1)	1
point over Q(a)/(a^4 - a^2 - 2*a + 1)	1
genus 1 curve (88a1)	1
point over Q(a)/(a^2 - a + 6)	1
point over Q(a)/(a^6 - 2a^5 + 2a^4 - 2a^2 + 3a - 1)	1
point over Q(a)/(a^7 - a^5 - 2a^4 + a^3 + 2a^2 - a - 1)	1
point over Q(a)/(a^6 - a^5 - 2a^4 + 2a^3 - 2*a + 1)	1
genus 1 curve x P^1	1
point over Q(a)/(a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)	1
point over Q(a)/(a^5 - a - 1)	1
unknown / not computed	1
point over Q(a)/(a^3 - a^2 + 4*a - 2)	1
uniruled elliptic threefold over P^1 x P^1, K_B + L = O(-1,0) - 0E (rationality undetermined)	1

Properties by bucket (number of matroids with the property)

	r2_n2	r2_n3	r2_n4	r2_n5	r2_n6	r2_n7	r2_n8	r3_n3	r3_n4	r3_n5	r3_n6	r3_n7	r3_n8	r3_n9	r3_n10	r3_n11	r3_n12	r4_n4	r4_n5	r4_n6	r4_n7	r4_n8	r4_n9
Uniform	1	1	—	—	—	—	—	1	1	1	—	—	—	—	—	—	—	1	1	1	1	—	—
Binary	1	3	6	10	16	23	32	1	4	10	22	43	77	131	213	333	507	1	5	16	43	106	240
Connected	0	1	2	4	7	11	17	0	1	4	15	52	187	901	8,687	288,341	31,600,478	0	1	7	52	731	188,961
Graphic	1	3	6	10	16	23	32	1	4	10	22	42	75	127	205	318	481	1	5	16	42	100	220
Paving	1	2	4	6	10	14	21	1	2	4	9	23	68	383	5,249	232,928	28,872,972	—	—	—	—	322	147,163
Quaternary	1	3	7	13	22	34	51	1	4	13	37	92	218	504	1,144	2,575	5,778	1	5	22	92	393	1,812
Regular	1	3	6	10	16	23	32	1	4	10	22	42	75	127	205	318	481	1	5	16	42	100	221
Simple	1	1	1	1	1	1	1	1	2	4	9	23	68	383	5,249	232,928	28,872,972	1	3	11	49	617	185,981
Ternary	1	3	7	12	20	30	44	1	4	12	31	70	148	299	579	1,085	1,989	1	5	20	70	238	776
Self dual	—	—	3	0	0	0	0	—	—	—	13	0	0	0	0	0	0	—	—	—	—	248	0
Series parallel	—	—	1	2	3	4	5	—	—	—	4	8	14	23	36	54	78	—	—	—	—	19	42
Transversal	—	—	7	13	22	34	50	—	—	—	37	92	209	442	873	1,627	2,886	—	—	—	—	432	1,804
Orientable	—	—	—	—	—	—	—	1	4	13	38	107	320	1,244	9,730	287,377	29,790,300	—	—	—	107	904	177,795
Free realization space	—	—	—	—	—	—	—	1	4	13	38	107	320	1,238	9,483	244,162	15,647,547	1	5	23	107	870	127,011
Realization space: is regular scheme	—	—	—	—	—	—	—	1	4	13	38	108	325	1,275	10,035	298,160	—	—	—	—	—	—	—
Realization space: smooth over ℤ	—	—	—	—	—	—	—	1	4	13	38	107	320	1,248	9,807	288,824	29,208,978	—	—	—	—	—	—
Supersolvable	—	—	—	—	—	—	—	—	3	9	23	54	119	260	564	1,250	2,947	—	3	10	30	86	235
Three lines	—	—	—	—	—	—	—	—	—	—	0	1	1	10	151	16,234	4,791,932	—	—	—	—	—	—

— = not computed for this bucket.