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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 12,651–12,700

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.177563	4	9	107	2	✓	∅	-1	empty
4.9.177562	4	9	104	1	✓	all	3	rational
4.9.177561	4	9	104	2	✓	all	2	empty
4.9.177560	4	9	105	1	✓	∅	-1	rational
4.9.177559	4	9	106	1	✓	∅	-1	point over Q(a)/(a^2 - 2)
4.9.177558	4	9	106	1	✓	all	2	point over Q(a)/(a^2 + 1)
4.9.177557	4	9	106	1	✓	∅	-1	empty
4.9.177556	4	9	107	1	✓	all	3	rational
4.9.177555	4	9	105	1	✓	all	2	empty
4.9.177554	4	9	105	1	✓	all but 2	1	empty
4.9.177553	4	9	106	1	✓	∅	-1	empty
4.9.177552	4	9	106	1	✓	all	4	empty
4.9.177551	4	9	106	1	✓	all but 2	1	empty
4.9.177550	4	9	106	1	✓	∅	-1	empty
4.9.177549	4	9	107	1	✓	all	2	empty
4.9.177548	4	9	106	1	✓	∅	-1	rational
4.9.177547	4	9	106	1	✓	all	2	empty
4.9.177546	4	9	106	1	✓	all	2	rational
4.9.177545	4	9	107	1	✓	∅	-1	rational
4.9.177544	4	9	107	1	✓	all	1	rational
4.9.177543	4	9	107	1	✓	all	1	rational
4.9.177542	4	9	107	1	✓	all but 2	2	rational
4.9.177541	4	9	107	1	✓	∅	-1	empty
4.9.177540	4	9	108	1	✓	{2}	-1	rational
4.9.177539	4	9	103	2	✓	all	3	empty
4.9.177538	4	9	104	2	✓	∅	-1	point over Q(a)/(a^2 - a + 1)
4.9.177537	4	9	105	2	✓	all	0	empty
4.9.177536	4	9	105	1	✓	all	1	empty
4.9.177535	4	9	106	1	✓	all	2	point over Q(a)/(a^2 + 1)
4.9.177534	4	9	105	2	✓	{2}	-1	empty
4.9.177533	4	9	106	1	✓	∅	-1	empty
4.9.177532	4	9	106	2	✓	all	1	empty
4.9.177531	4	9	107	2	✓	∅	-1	rational
4.9.177530	4	9	103	4	✓	∅	-1	empty
4.9.177529	4	9	104	2	✓	all	3	empty
4.9.177528	4	9	105	2	✓	all	3	empty
4.9.177527	4	9	105	2	✓	all	3	empty
4.9.177526	4	9	106	2	✓	all	3	empty
4.9.177525	4	9	106	2	✓	all	2	point over Q(a)/(a^2 - a + 1)
4.9.177524	4	9	106	2	✓	all	1	rational
4.9.177523	4	9	107	2	✓	∅	-1	rational
4.9.177522	4	9	104	1	✓	∅	-1	point over Q(a)/(a^2 - a - 1)
4.9.177521	4	9	104	2	✓	∅	-1	empty
4.9.177520	4	9	105	1	✓	all	1	rational
4.9.177519	4	9	106	1	✓	∅	-1	rational
4.9.177518	4	9	106	1	✓	all	1	rational
4.9.177517	4	9	107	1	✓	all	0	rational
4.9.177516	4	9	106	1	✓	all	2	point over Q(a)/(a^2 - 2)
4.9.177515	4	9	106	1	✓	∅	-1	point over Q(a)/(a^2 - a - 1)
4.9.177514	4	9	106	1	✓	all but 2	1	empty