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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 11,651–11,700

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.178563	4	9	103	2	✓	all but 2	1	rational
4.9.178562	4	9	103	1	✓	all	2	rational
4.9.178561	4	9	104	2	✓	all	2	rational
4.9.178560	4	9	101	4	✓	all	3	rational
4.9.178559	4	9	102	2	✓	all	2	rational
4.9.178558	4	9	103	1	✓	∅	-1	rational
4.9.178557	4	9	104	4	✓	all	2	rational
4.9.178556	4	9	102	12	✓	all	2	rational
4.9.178555	4	9	103	2	✓	all	3	rational
4.9.178554	4	9	104	2	✓	all	3	rational
4.9.178553	4	9	105	12	✓	all	0	rational
4.9.178552	4	9	102	2	✓	∅	-1	empty
4.9.178551	4	9	103	2	✓	all	1	empty
4.9.178550	4	9	102	1	✓	all	4	empty
4.9.178549	4	9	103	1	✓	all but 2,3	0	empty
4.9.178548	4	9	103	1	✓	all but 2	2	empty
4.9.178547	4	9	104	1	✓	∅	-1	empty
4.9.178546	4	9	103	1	✓	all	2	empty
4.9.178545	4	9	104	2	✓	all	3	empty
4.9.178544	4	9	104	2	✓	all	2	empty
4.9.178543	4	9	104	1	✓	∅	-1	empty
4.9.178542	4	9	105	2	✓	∅	-1	empty
4.9.178541	4	9	100	48	✓	all	1	empty
4.9.178540	4	9	101	16	✓	all	2	empty
4.9.178539	4	9	102	16	✓	all	3	empty
4.9.178538	4	9	103	4	✓	all	2	empty
4.9.178537	4	9	104	4	✓	all but 2	2	empty
4.9.178536	4	9	103	16	✓	all but 2	2	empty
4.9.178535	4	9	104	8	✓	∅	-1	empty
4.9.178534	4	9	105	16	✓	all but 2	1	empty
4.9.178533	4	9	100	6	✓	all but 2	2	empty
4.9.178532	4	9	101	2	✓	all but 2	1	empty
4.9.178531	4	9	102	2	✓	{2}	-1	empty
4.9.178530	4	9	103	1	✓	∅	-1	empty
4.9.178529	4	9	104	1	✓	∅	-1	empty
4.9.178528	4	9	103	2	✓	all but 2	3	empty
4.9.178527	4	9	104	1	✓	all	1	empty
4.9.178526	4	9	105	2	✓	all but 2	2	empty
4.9.178525	4	9	101	6	✓	all	3	empty
4.9.178524	4	9	102	2	✓	all but 2	1	empty
4.9.178523	4	9	103	2	✓	all but 2	0	empty
4.9.178522	4	9	104	1	✓	all	1	empty
4.9.178521	4	9	105	1	✓	all	2	empty
4.9.178520	4	9	104	1	✓	all	2	empty
4.9.178519	4	9	105	1	✓	all but 2	1	empty
4.9.178518	4	9	104	2	✓	all but 3	1	empty
4.9.178517	4	9	105	1	✓	all	2	empty
4.9.178516	4	9	106	2	✓	∅	-1	empty
4.9.178515	4	9	101	2	✓	all	2	empty
4.9.178514	4	9	102	2	✓	all but 2,3	0	empty