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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 4,651–4,700

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.185563	4	9	105	4	✓	∅	-1	rational
4.9.185562	4	9	104	6	✓	all	1	rational
4.9.185561	4	9	105	12	✓	all	3	rational
4.9.185560	4	9	104	2	✓	∅	-1	rational
4.9.185559	4	9	105	2	✓	all	2	rational
4.9.185558	4	9	104	1	✓	all	4	rational
4.9.185557	4	9	105	2	✓	all	2	rational
4.9.185556	4	9	105	2	✓	all	3	rational
4.9.185555	4	9	105	4	✓	all	5	rational
4.9.185554	4	9	106	4	✓	all	6	rational
4.9.185553	4	9	104	2	✓	all	1	rational
4.9.185552	4	9	104	2	✓	all	2	rational
4.9.185551	4	9	105	2	✓	all	3	rational
4.9.185550	4	9	105	6	✓	all	2	rational
4.9.185549	4	9	104	1	✓	all	3	rational
4.9.185548	4	9	105	1	✓	all but 2	1	rational
4.9.185547	4	9	105	2	✓	all but 2	1	rational
4.9.185546	4	9	105	2	✓	∅	-1	rational
4.9.185545	4	9	106	2	✓	∅	-1	rational
4.9.185544	4	9	104	2	✓	∅	-1	rational
4.9.185543	4	9	105	4	✓	all	4	rational
4.9.185542	4	9	104	1	✓	all	2	rational
4.9.185541	4	9	105	2	✓	all but 2	1	rational
4.9.185540	4	9	105	1	✓	all	1	rational
4.9.185539	4	9	105	2	✓	all	3	rational
4.9.185538	4	9	106	2	✓	all	3	rational
4.9.185537	4	9	105	2	✓	all	3	rational
4.9.185536	4	9	106	4	✓	all	2	rational
4.9.185535	4	9	106	4	✓	all	4	rational
4.9.185534	4	9	106	4	✓	∅	-1	rational
4.9.185533	4	9	107	8	✓	all	1	rational
4.9.185532	4	9	99	72	✓	∅	-1	rational
4.9.185531	4	9	103	72	✓	∅	-1	rational
4.9.185530	4	9	104	12	✓	∅	-1	rational
4.9.185529	4	9	105	36	✓	all	2	rational
4.9.185528	4	9	105	4	✓	all	2	rational
4.9.185527	4	9	106	12	✓	∅	-1	rational
4.9.185526	4	9	106	8	✓	all	3	rational
4.9.185525	4	9	106	24	✓	∅	-1	rational
4.9.185524	4	9	107	24	✓	all	2	rational
4.9.185523	4	9	102	216	✓	all	2	rational
4.9.185522	4	9	107	72	✓	all	3	rational
4.9.185521	4	9	107	72	✓	all	3	rational
4.9.185520	4	9	108	216	✓	all but 2	2	rational
4.9.185519	4	9	60	4320	✗	all	5	rational
4.9.185518	4	9	80	240	✗	all but 2,5	0	rational
4.9.185517	4	9	84	96	✗	all but 2	1	rational
4.9.185516	4	9	86	32	✗	all	4	rational
4.9.185515	4	9	88	96	✗	all	2	rational
4.9.185514	4	9	90	1440	✗	all	4	rational