Minimal Cover
A minimal cover is a Cover for which removal of one member destroys the covering property. Let 
be thenumber of minimal covers of 
with 
members. Then
where
is a Binomial Coefficient, 
is a Stirling Number of the Second Kind, and
Special cases include
and 
. |  |  |  |  |  |  |  |
| Sloane | Sloane's A000392 | Sloane's A003468 | Sloane's A016111 | ||||
| 1 | 1 | ||||||
| 2 | 1 | 1 | |||||
| 3 | 1 | 6 | 1 | ||||
| 4 | 1 | 25 | 22 | 1 | |||
| 5 | 1 | 90 | 305 | 65 | 1 | ||
| 6 | 1 | 301 | 3410 | 2540 | 171 | 1 | |
| 7 | 1 | 966 | 33621 | 77350 | 17066 | 420 | 1 |
References
Hearne, T. and Wagner, C. ``Minimal Covers of Finite Sets.'' Disc. Math. 5, 247-251, 1973. Macula, A. J. ``Lewis Carroll and the Enumeration of Minimal Covers.'' Math. Mag. 68, 269-274, 1995.
- Regular Point
- Regular Polygon
- Regular Polyhedron
- Regular Prime
- Regular Ring
- Regular Sequence
- Regular Singularity
- Regular Singular Point
- Regular Surface
- Regular Triangle Center
- Regulus
- Reidemeister Moves
- Reidemeister's Theorem
- Reinhardt Domain
- Relation
- Relative Error
- Relative Extremum
- Relatively Prime
- Relative Maximum
- Relative Minimum
- Relaxation Methods
- Remainder
- Remainder Theorem
- Rembs' Surfaces
- Removable Crossing