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Size rank n

Invariants Bases Automorphisms Dimension of realization space Girth Expected dimension over ℤ

Realizability realizable in char 0 realizable in characteristic char set class birational type

Properties Simple Connected Paving Uniform Regular Binary Ternary Quaternary Graphic Transversal Series parallel Self dual Orientable Supersolvable Three lines Free realization space Realization space: smooth over ℤ Realization space: is regular scheme

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1,812 matroids, showing 1–50

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.60571	4	9	112	48	✓	all	4	rational over Q(a)/(a^2 - a + 1)
4.9.107208	4	9	110	4	✓	all	3	empty
4.9.107269	4	9	110	8	✓	all	3	empty
4.9.107647	4	9	111	2	✓	all	4	empty
4.9.144126	4	9	109	8	✓	all	4	empty
4.9.144383	4	9	108	4	✓	all	1	point over Q(a)/(a^2 - a - 1)
4.9.144639	4	9	108	2	✓	all but 2	1	empty
4.9.144693	4	9	108	8	✓	all	4	empty
4.9.145589	4	9	108	64	✓	all	1	rational
4.9.145898	4	9	109	4	✓	all but 2	2	point over Q(a)/(a^2 - a + 1)
4.9.145957	4	9	109	2	✓	all	3	empty
4.9.151415	4	9	108	3	✓	all	3	empty
4.9.151450	4	9	104	192	✓	all	1	empty
4.9.152859	4	9	107	12	✓	all but 2	0	point over Q(a)/(a^2 - a + 1)
4.9.152865	4	9	105	12	✓	all but 2	1	rational
4.9.152949	4	9	107	2	✓	all but 2	1	point over Q(a)/(a^2 - a - 1)
4.9.153026	4	9	106	4	✓	all	4	empty
4.9.155077	4	9	106	8	✓	all	2	empty
4.9.160083	4	9	106	24	✓	all	3	empty
4.9.161527	4	9	108	8	✓	all	1	empty
4.9.163927	4	9	104	4	✓	all	2	empty
4.9.164016	4	9	107	1	✓	all	3	empty
4.9.165394	4	9	107	2	✓	all	2	point over Q(a)/(a^2 - a + 1)
4.9.165459	4	9	104	8	✓	all but 2	1	empty
4.9.167022	4	9	106	2	✓	all	1	empty
4.9.167090	4	9	106	8	✓	all	3	empty
4.9.167171	4	9	102	12	✓	all but 2	1	point over Q(a)/(a^2 - a + 1)
4.9.167780	4	9	106	2	✓	all	1	empty
4.9.167822	4	9	104	24	✓	all	2	empty
4.9.168719	4	9	106	1	✓	all but 2,5	0	empty
4.9.168849	4	9	106	8	✓	∅	-1	empty
4.9.169801	4	9	105	1	✓	all	2	empty
4.9.169894	4	9	104	2	✓	all	1	empty
4.9.169957	4	9	104	1	✓	∅	-1	empty
4.9.170009	4	9	102	2	✓	all	5	point over Q(a)/(a^2 - a + 1)
4.9.170050	4	9	105	1	✓	∅	-1	point over Q(a)/(a^2 - a + 1)
4.9.170267	4	9	103	2	✓	∅	-1	rational
4.9.170467	4	9	101	2	✓	all	2	rational
4.9.170494	4	9	102	1	✓	all	3	point over Q(a)/(a^2 - a - 1)
4.9.170539	4	9	102	2	✓	all	5	empty
4.9.173283	4	9	105	2	✓	all	2	empty
4.9.173330	4	9	105	2	✓	∅	-1	empty
4.9.173450	4	9	106	2	✓	∅	-1	point over Q(a)/(a^2 - a + 1)
4.9.173597	4	9	105	1	✓	all	3	point over Q(a)/(a^2 - a - 1)
4.9.173645	4	9	101	2	✓	all	3	rational
4.9.173686	4	9	103	2	✓	all	3	point over Q(a)/(a^2 - a - 1)
4.9.173695	4	9	100	4	✓	all	2	rational
4.9.175298	4	9	103	1	✓	∅	-1	point over Q(a)/(a^2 - a - 1)
4.9.175378	4	9	104	1	✓	∅	-1	empty
4.9.175395	4	9	104	4	✓	∅	-1	point over Q(a)/(a^2 - a + 1)