# Studies of Euler diagrams/blightless

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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 EC with arity up to 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

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.

### multi-bundle

6, 11, 15, 18, 19

### bundles

7, 12, 13, 16, 20, 21

## 4-ary

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.

### multi-bundle

34, 40, 77, 108, 117, 127, 214, 296, 297, 333, 347

### bundles

61, 84, 109, 116, 146, 157, 203, 220, 270, 271, 272, 281, 282, 306, 312, 317, 321, 346, 349, 353 374, 383, 384