VasCalc Results - ChordMod4T: Difference between revisions
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Revision as of 12:48, 10 July 2006
This page documents some computational results obtained by using the ChordsMod4T software component of the VasCalc project. We denote by the formal (rational) vector space generated by all chord diagrams with chords on a skeleton of lines and circles, modulo the relations. The algorithm is straightforward: first all such diagrams are constructed, then relations are introduced iteratively over all possible terms in a relation. See the documentation for further information about the program and how these results were generated.
Some Dimensions of
The tables below give the dimensions of for various values of , and . Each table corresponds to a fixed value of - that is, the number of chords.
This is work in progress - these numbers are not reliable yet!!!
Number of Lines | Number of Circles | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
0 | 0 | 2 | 8 | 24 | 59 | 125 | 237 | 413 | 674 | 1044 |
1 | 2 | 8 | 24 | 59 | 125 | 237 | 413 | 674 | 1044 | 1550 |
2 | 9 | 25 | 60 | 126 | 238 | 414 | 675 | 1045 | 1551 | 2223 |
3 | 28 | 63 | 129 | 241 | 417 | 678 | 1048 | 1554 | 2226 | 3097 |
4 | 69 | 135 | 247 | 423 | 684 | 1054 | 1560 | 2232 | 3103 | 4209 |
5 | 145 | 257 | 433 | 694 | 1064 | 1570 | 2242 | 3113 | 4219 | 5599 |
6 | 272 | 448 | 709 | 1079 | 1585 | 2257 | 3128 | 4234 | 5614 | 7310 |
7 | 469 | 730 | 1100 | 1606 | 2278 | 3149 | 4255 | 5635 | 7331 | 9388 |
8 | 758 | 1128 | 1634 | 2306 | 3177 | 4283 | 5663 | 7359 | 9416 | 11882 |
9 | 1164 | 1670 | 2342 | 3213 | 4319 | 5699 | 7395 | 9452 | 11918 | 14844 |
Number of Lines | Number of Circles | ||||||
---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | |
0 | 0 | 3 | 19 | 80 | 270 | 770 | 1918 |
1 | 3 | 19 | 80 | 270 | 770 | 1918 | 4284 |
2 | 23 | 88 | 283 | 789 | 1944 | 4318 | 8803 |
3 | 111 | 321 | 845 | 2021 | 4419 | 8931 | 16876 |
4 | 394 | 954 | 2172 | 4618 | 9184 | 17189 | |
5 | 1130 | 2418 | 4944 | 9600 | 17705 | 31125 |
Number of Lines | Number of Circles | |||||
---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | ||
0 | 0 | 6 | 44 | 241 | 1063 | |
1 | 6 | 44 | 241 | 1063 | 3930 | |
2 | 60 | 283 | 1160 | 4126 |