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Universal layered permutations. (English) Zbl 1393.05003

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)].

MSC:

05A05 Permutations, words, matrices
06A07 Combinatorics of partially ordered sets

Citations:

Zbl 1316.05001

Software:

OEIS
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Full Text: arXiv Link

References:

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[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
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[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
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