Cover
A group 
of Subsets of 
whose Union contains the given set (
) iscalled a cover (or a Covering). A Minimal Cover is a cover for which removal of one member destroysthe covering property. There are various types of specialized covers, including proper covers, antichain covers, minimalcovers, 
-covers, and 
-covers. The number of possible covers for a set of 
elements is
the first few of which are 1, 5, 109, 32297, 2147321017, 9223372023970362989, ... (Sloane's A003465).The number of proper covers for a set of
elements is |  |  | |
|  |
the first few of which are 0, 1, 45, 15913, 1073579193, ... (Sloane's A007537).See also Minimal Cover
References
Eppstein, D. ``Covering and Packing.''http://www.ics.uci.edu/~eppstein/junkyard/cover.html. Macula, A. J. ``Covers of a Finite Set.'' Math. Mag. 67, 141-144, 1994. Sloane, N. J. A. SequencesA003465/M4024and A007537/M5287in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Roth's Removal Rule
- Roth's Theorem
- Rotkiewicz Theorem
- Rotoinversion
- Rotor
- Rotunda
- Rouché's Theorem
- Roulette
- Round
- Rounding
- Routh-Hurwitz Theorem
- Routh's Theorem
- RSA Encryption
- RSA Number
- Rubber-Sheet Geometry
- Rubik's Clock
- Rubik's Cube
- Rudin-Shapiro Sequence
- Rudvalis Group
- Rule
- Ruled Surface
- Rule of 72
- Ruler
- Ruler Function
- Ruling