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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 1,501–1,550

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.188713	4	9	52	4	✗	all	2	rational
4.9.188712	4	9	53	1	✗	all	1	rational
4.9.188711	4	9	54	2	✗	all	5	rational
4.9.188710	4	9	53	2	✗	∅	-1	rational
4.9.188709	4	9	54	2	✗	∅	-1	rational
4.9.188708	4	9	54	2	✗	{2}	-1	rational
4.9.188707	4	9	54	2	✗	all	3	rational
4.9.188706	4	9	54	1	✗	all	3	rational
4.9.188705	4	9	55	1	✗	all but 2	2	rational
4.9.188704	4	9	55	4	✗	all	5	rational
4.9.188703	4	9	56	8	✗	all	3	rational
4.9.188702	4	9	48	24	✗	∅	-1	rational
4.9.188701	4	9	53	4	✗	all	3	rational
4.9.188700	4	9	54	8	✗	all	1	empty
4.9.188699	4	9	55	8	✗	all	5	rational
4.9.188698	4	9	54	4	✗	all	1	rational
4.9.188697	4	9	55	4	✗	all	3	rational
4.9.188696	4	9	55	2	✗	all	3	rational
4.9.188695	4	9	56	2	✗	∅	-1	rational
4.9.188694	4	9	56	8	✗	∅	-1	rational
4.9.188693	4	9	57	8	✗	all	1	rational
4.9.188692	4	9	51	12	✗	∅	-1	rational
4.9.188691	4	9	54	12	✗	all	6	rational
4.9.188690	4	9	55	2	✗	all	3	rational
4.9.188689	4	9	56	2	✗	all	3	rational
4.9.188688	4	9	56	2	✗	all but 2	1	rational
4.9.188687	4	9	56	2	✗	all but 2,3,5,7	0	rational
4.9.188686	4	9	57	2	✗	all	1	rational
4.9.188685	4	9	56	4	✗	all	4	rational
4.9.188684	4	9	57	4	✗	all	4	rational
4.9.188683	4	9	57	4	✗	all	2	rational
4.9.188682	4	9	57	2	✗	all	1	rational
4.9.188681	4	9	58	4	✗	all but 2,5	0	rational
4.9.188680	4	9	54	48	✗	all	1	rational
4.9.188679	4	9	58	48	✗	all	2	rational
4.9.188678	4	9	58	12	✗	all	1	rational
4.9.188677	4	9	59	48	✗	all	3	rational
4.9.188676	4	9	51	12	✗	∅	-1	rational
4.9.188675	4	9	54	8	✗	all	1	empty
4.9.188674	4	9	54	4	✗	all	3	rational
4.9.188673	4	9	55	2	✗	all	1	rational
4.9.188672	4	9	55	2	✗	∅	-1	rational
4.9.188671	4	9	56	2	✗	all but 2	1	rational
4.9.188670	4	9	56	8	✗	∅	-1	rational
4.9.188669	4	9	56	4	✗	all but 2,5	0	rational
4.9.188668	4	9	57	4	✗	all but 2,7	0	rational
4.9.188667	4	9	54	48	✗	all	3	rational
4.9.188666	4	9	58	48	✗	∅	-1	rational
4.9.188665	4	9	53	4	✗	all	2	rational
4.9.188664	4	9	54	12	✗	∅	-1	rational