- Random matrices and pentagonal numbers May 25, 2013
- About problem setting May 8, 2013
- Asymptotics and generating functions April 29, 2013
- Catalan numbers, mirror image and walks enumeration April 23, 2013
- Enumeration of Antimatroids, part IV April 19, 2013
- Antimatroid Asymptotic analysis Ballow walks binary matrices binary vectors Breadth-first search C++ Catalan number Codechef Competition Competitions enumeration Euler Family of sets Games and Puzzles generating function Hashtable Mask (computing) Mutual exclusion Parallel computing partitions pentagonal numbers Permutation Problem setting Problem solving Programming Programming competitions Programming contests Recreations Symmetry Threads TopCoder Training
- 1,601 visits (since 06.04.2013)
Tag Archives: Family of sets
Recently I found an interesting problem: enumeration of possible antimatroids over finite set.
From combinatorial point of view, an antimatroid is a family of sets, with special properties.
Following the wikipedia definition, is an antimatroid iff:
- is closed under unions, that is:
- is a nonempty accesible:
For example, following family is an antimatroid:
From now, I will denote the largest set, being also a superset of every other one in the family, as (so in previous example, ).