Studies of Euler diagrams/blightless
Blightless functions are those that are not blighted.
One could say, that only they deserve to be drawn as Euler diagrams. (While the blight is easier to express separately.)
For geometric analysis, only those with a single bundle are interesting.
Eventually these pages should show an example for each clan with arity 4.
The following triangle shows the numbers of ECs by arity (rows) and number of bundles (columns). (compare sequences)
0 1 2 3 4 blightless (row sums) blighted all (A000618) 0 2 2 0 2 1 0 0 0 1 1 2 0 0 1 1 2 3 3 0 6 2 3 11 5 16 4 0 292 36 10 5 343 37 380 298 357 45 402
3-ary
[edit | edit source]Of the 22 BECs with arity up to 3 there are 16 whose actual arity is 3.
5 of them are blighted, and 11 are blightless. 5 of them have multiple bundles, and 6 have only one.
4-ary
[edit | edit source]Of the 402 BECs with arity up to 4 there are 380 whose actual arity is 4.
37 of them are blighted, and 343 are blightless. 51 of them have multiple bundles, and 292 have only one.
34, 40, 77, 108, 117, 127, 214, 296, 297, 333, 347
61, 84, 109, 116, 146, 157, 203, 220, 270, 271, 272, 281, 282, 306, 312, 317, 321, 346, 349, 353 374, 383, 384
