Separating Family
A Separating Family is a Set of Subsets in which each pair of adjacent elements are found separated,each in one of two disjoint subsets. The 26 letters of the alphabet can be separated by a family of 9,
The minimal size of the separating family for an
-set is 0, 2, 3, 4, 5, 5, 6, 6, 6, 7, 7, 7, ... (Sloane's A007600).See also Katona's Problem
References
Honsberger, R. ``Cai Mao-Cheng's Solution to Katona's Problem on Families of Separating Subsets.'' Ch. 18 in Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 224-239, 1985. Sloane, N. J. A. SequenceA007600/M0456in ``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.
- Reciprocating Sphere
- Reciprocation
- Reciprocity Theorem
- Rectangle
- Rectangle Function
- Rectangle Squaring
- Rectangular Coordinates
- Rectangular Distribution
- Rectangular Hyperbola
- Rectangular Parallelepiped
- Rectangular Projection
- Rectifiable Current
- Rectifiable Set
- Rectification
- Rectifying Latitude
- Rectifying Plane
- Recurrence Relation
- Recurrence Sequence
- Recurring Digital Invariant
- Recursion
- Recursive Function
- Recursive Monotone Stable Quadrature
- Red-Black Tree
- Red Net
- Reduced Amicable Pair