Hypothesized counts:

N    # sigmas
---  --------
0     1  /     1
1     1  /     4
2     2  /    16
3     5? /   256
4    15? / 65536

================================================================
X = (): sigmas =
0

----------------------------------------------------------------
X = (a): sigmas =
0  a

----------------------------------------------------------------
X = (a b): sigmas =
0  . .  ab
0  a b  ab

----------------------------------------------------------------
X = (a b c): sigmas =
0  . . .  .. .. ..  abc
0  a . .  .. .. bc  abc
0  . b .  .. ac ..  abc
0  . . c  ab .. ..  abc
0  a b c  ab ac bc  abc

----------------------------------------------------------------
X = (a b c d): sigmas = ??
0  . . . .  .. .. .. .. .. ..  ... ... ... ...  abcd

0  a . . .  .. .. .. .. .. ..  ... ... ... bcd  abcd
0  . b . .  .. .. .. .. .. ..  ... ... acd ...  abcd
0  . . c .  .. .. .. .. .. ..  ... abd ... ...  abcd
0  . . . d  .. .. .. .. .. ..  abc ... ... ...  abcd

0  . . . .  ab .. .. .. .. cd  ... ... ... ...  abcd
0  . . . .  .. ac .. .. bd ..  ... ... ... ...  abcd
0  . . . .  .. .. ad bc .. ..  ... ... ... ...  abcd

0  a b . .  ab .. .. .. .. cd  ... ... acd bcd  abcd
0  a . c .  .. ac .. .. bd ..  ... abd ... bcd  abcd
0  a . . d  .. .. ad bc .. ..  abc ... ... bcd  abcd
0  . b c .  .. .. ad bc .. ..  ... abd acd ...  abcd
0  . b . d  .. ac .. .. bd ..  abc ... acd ...  abcd
0  . . c d  ab .. .. .. .. cd  abc abd ... ...  abcd

??

0  a b c d  ab ac ad bc bd cd  abc abd acd bcd  abcd