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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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32,400,859 matroids, showing 4,751–4,800

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.185463	4	9	104	4	✓	all	2	rational
4.9.185462	4	9	105	1	✓	all	1	rational
4.9.185461	4	9	104	2	✓	all but 2	0	rational
4.9.185460	4	9	104	4	✓	all	4	rational
4.9.185459	4	9	104	2	✓	all but 2	2	rational
4.9.185458	4	9	105	1	✓	all	5	rational
4.9.185457	4	9	105	2	✓	{3}	-1	rational
4.9.185456	4	9	105	1	✓	∅	-1	rational
4.9.185455	4	9	105	2	✓	all	3	rational
4.9.185454	4	9	106	2	✓	all	3	rational
4.9.185453	4	9	106	4	✓	all	1	rational
4.9.185452	4	9	106	8	✓	all	3	rational
4.9.185451	4	9	106	2	✓	all	3	rational
4.9.185450	4	9	106	2	✓	∅	-1	rational
4.9.185449	4	9	107	4	✓	all	4	rational
4.9.185448	4	9	108	96	✓	all	3	rational
4.9.185447	4	9	99	96	✓	all	4	rational
4.9.185446	4	9	103	12	✓	all	0	rational
4.9.185445	4	9	103	12	✓	all but 2	2	rational
4.9.185444	4	9	103	4	✓	all	3	rational
4.9.185443	4	9	104	4	✓	all	3	rational
4.9.185442	4	9	104	16	✓	all but 2	2	rational
4.9.185441	4	9	105	16	✓	all	3	rational
4.9.185440	4	9	104	24	✓	all	1	empty
4.9.185439	4	9	105	48	✓	all	2	empty
4.9.185438	4	9	104	2	✓	∅	-1	rational
4.9.185437	4	9	105	2	✓	all	5	rational
4.9.185436	4	9	105	8	✓	∅	-1	rational
4.9.185435	4	9	105	4	✓	all	1	rational
4.9.185434	4	9	106	8	✓	all	2	rational
4.9.185433	4	9	105	2	✓	all	3	rational
4.9.185432	4	9	105	4	✓	all	1	rational
4.9.185431	4	9	105	2	✓	∅	-1	rational
4.9.185430	4	9	106	2	✓	∅	-1	rational
4.9.185429	4	9	106	16	✓	∅	-1	rational
4.9.185428	4	9	106	8	✓	∅	-1	rational
4.9.185427	4	9	107	16	✓	all	4	rational
4.9.185426	4	9	104	2	✓	all but 2	0	rational
4.9.185425	4	9	105	2	✓	all	2	rational
4.9.185424	4	9	105	6	✓	all	3	rational
4.9.185423	4	9	105	1	✓	all	3	rational
4.9.185422	4	9	105	2	✓	all but 2	2	rational
4.9.185421	4	9	106	2	✓	all	4	rational
4.9.185420	4	9	105	2	✓	all	5	rational
4.9.185419	4	9	105	1	✓	all but 2	2	rational
4.9.185418	4	9	105	1	✓	all	4	rational
4.9.185417	4	9	106	1	✓	all	5	rational
4.9.185416	4	9	104	6	✓	∅	-1	rational
4.9.185415	4	9	105	6	✓	all	3	rational
4.9.185414	4	9	105	2	✓	all	3	rational