Partitions with Restricted Block Sizes, Möbius Functions and the k-of-each Problem.
Please always quote using this URN: urn:nbn:de:0297-zib-1363
- {\newcommand{\R} {{\rm {\mbox{\protect\makebox[.15em][l]{I}R}}}} Given a list of $n$ numbers in $\R $, one wants to decide wether every number in the list occurs at least $k$ times. I will show that $(1-\epsilon)n\log_3(n/k)$ is a lower bound for the depth of a linear decision tree determining this problem. This is done by using the Björner-Lov\'asz method, which turns the problem into one of estimating the Möbius function for a certain partition lattice. I will also calculate the exponential generating function for the Möbius function of a partition poset with restricted block sizes in general.}
Author: | Svante Linusson |
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Document Type: | ZIB-Report |
Date of first Publication: | 1994/03/10 |
Series (Serial Number): | ZIB-Report (SC-94-06) |
ZIB-Reportnumber: | SC-94-06 |
Published in: | Appeared in: SIAM Journal on Discrete Mathematics 10 (1997) 18-29 |