A minimal cover is a Cover for which removal of one member destroys the covering property. Let be the
number 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.

© 1996-9

1999-05-26