VasCalc Results - ChordMod4T

This page documents some computational results obtained by using the ChordsMod4T software component of the VasCalc project. We denote by A(l,m,n) the formal vector space of chord diagrams with n chords on a skeleton of l lines and m circles, modulo the 4T relations.

Some Dimensions of A(l,m,n)

Dimensions of chord diagram spaces with 2 chords

Number of Lines	Number of Circles
	0	1	2	3	4	5	6	7	8	9
0	0	2	8	27	69	145	272	469	758	1164
1	2	8	26	68	145	272	469	758	1164	1715
2	9	25	66	144	272	469	758	1164	1715	2442
3	28	63	141	271	469	758	1164	1715	2442	3379
4	69	135	267	468	758	1164	1715	2442	3379	4563
5	145	257	463	757	1164	1715	2442	3379	4563	6034
6	272	448	751	1163	1715	2442	3379	4563	6034	7835
7	469	730	1156	1714	2442	3379	4563	6034	7835	10012

Dimensions of chord diagram spaces with 3 chords

Number of Lines	Number of Circles
	0	1	2	3	4	5	6
0	0	3	19	92	370	1120	2778
1	3	19	88	351	1096	2768	6083
2	23	88	329	1053	2734	6073	12176
3	111	321	991	2657	6029	12166	22689
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