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COMBINATORICS
2000
107views more  COMBINATORICS 2000»
13 years 7 months ago
Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs
A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting ...
Martin Klazar
CORR
2011
Springer
156views Education» more  CORR 2011»
13 years 2 months ago
Impossibility of Succinct Quantum Proofs for Collision-Freeness
We show that any quantum algorithm to decide whether a function f : [n] → [n] is a permutation or far from a permutation must make Ω n1/3 /w queries to f, even if the algorith...
Scott Aaronson
SODA
2010
ACM
202views Algorithms» more  SODA 2010»
14 years 5 months ago
Counting Inversions, Offline Orthogonal Range Counting, and Related Problems
We give an O(n lg n)-time algorithm for counting the number of inversions in a permutation on n elements. This improves a long-standing previous bound of O(n lg n/ lg lg n) that ...
Timothy M. Chan, Mihai Patrascu
CDC
2010
IEEE
130views Control Systems» more  CDC 2010»
13 years 2 months ago
Controllability of homogeneous single-leader networks
This paper addresses an aspect of controllability in a single-leader network when the agents are homogeneous. In such a network, indices are not assigned to the individual agents a...
Philip Twu, Magnus Egerstedt, Simone Martini
EJC
2007
13 years 7 months ago
Symmetric functions, generalized blocks, and permutations with restricted cycle structure
We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theo...
Attila Maróti