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Inclusion-exclusion meets exclusion | | Marcel Wild
; | | Date: |
26 Sep 2013 | | Abstract: | Some "principle of exclusion" (POE) has been introduced and investigated by
the author in previous publications. In particular the POE often outperforms
the familiar principle of inclusion-exclusion (IE), provided both are
applicable. In the present article we argue that sometimes the two can join
hands. That is, POE doesn’t replace IE but rather accelerates the otherwise
infeasible IE calculations. The ideas are applied to count (a) constrained
permutations (constrained in a way more general than by forbidden positions),
(b) integer partitions, and (c) models of a Boolean function given in DNF.
Concerning (c), for several choices of parameters binary decision diagrams are
not competitive, and they never are competitive when only models (=bitstrings)
of fixed weight need to be counted. | | Source: | arXiv, 1309.6927 | | Services: | Forum | Review | PDF | Favorites | |
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