Albert, Michael; Engen, Michael; Pantone, Jay; Vatter, Vincent Universal layered permutations. (English) Zbl 1393.05003 Electron. J. Comb. 25, No. 3, Research Paper P3.23, 5 p. (2018). Summary: We establish an exact formula for the length of the shortest permutation containing all layered permutations of length \(n\), proving a conjecture of D. Gray [Graphs Comb. 31, No. 4, 941–952 (2015; Zbl 1316.05001)]. Cited in 1 ReviewCited in 2 Documents MSC: 05A05 Permutations, words, matrices 06A07 Combinatorics of partially ordered sets Keywords:permutation patterns; universal permutations Citations:Zbl 1316.05001 Software:OEIS PDFBibTeX XMLCite \textit{M. Albert} et al., Electron. J. Comb. 25, No. 3, Research Paper P3.23, 5 p. (2018; Zbl 1393.05003) Full Text: arXiv Link References: [1] M. J. Bannister, Z. Cheng, W. E. Devanny, and D. Eppstein. Superpatterns and universal point sets. J. Graph Algorithms Appl., 18(2):177-209, 2014. · Zbl 1290.05142 [2] H. Eriksson, K. Eriksson, S. Linusson, and J. W¨astlund. Dense packing of patterns in a permutation. Ann. Comb., 11(3-4):459-470, 2007. · Zbl 1141.05004 [3] D. Gray. Bounds on superpatterns containing all layered permutations. Graphs Combin., 31(4):941-952, 2015. · Zbl 1316.05001 [4] D. E. Knuth. The Art of Computer Programming, Volume 3. Addison-Wesley, Reading, Massachusetts, 1973. · Zbl 0302.68010 [5] A. Miller. Asymptotic bounds for permutations containing many different patterns. J. Combin. Theory Ser. A, 116(1):92-108, 2009. · Zbl 1177.05012 [6] The On-line Encyclopedia of Integer Sequences (OEIS). Published electronically at http://oeis.org/. the electronic journal of combinatorics 25(3) (2018), #P3.235 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.