Albert, M. H.; Coleman, Micah; Flynn, Ryan; Leader, Imre Permutations containing many patterns. (English) Zbl 1140.05002 Ann. Comb. 11, No. 3-4, 265-270 (2007). Summary: It is shown that the maximum number of patterns that can occur in a permutation of length \(n\) is asymptotically \(2^{n}\). This significantly improves a previous result of M. Coleman [Electron. J. Comb. 11, No. 1, Research paper N8 (2004; Zbl 1053.05002)]. Cited in 2 Documents MSC: 05A05 Permutations, words, matrices 05A16 Asymptotic enumeration 05D40 Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) Keywords:permutation patterns; probabilistic counting Citations:Zbl 1053.05002 PDFBibTeX XMLCite \textit{M. H. Albert} et al., Ann. Comb. 11, No. 3--4, 265--270 (2007; Zbl 1140.05002) Full Text: DOI arXiv