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Optimal Packing Behavior of Some 2-Block Patterns
Dan Warren
Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville FL 32611--8105, USA
warren@math.ufl.edu
Annals of Combinatorics 8 (3) p.355-367 September, 2004
AMS Subject Classification:05A15, 05A16
Abstract:
In this paper, a result of Albert, Atkinson, Handley, Holton, and Stromquist [1, Proposition 2.4] which characterizes the optimal packing behavior of the pattern 1243 is generalized in two directions. The packing densities of layered patterns of type are computed.

Keywords: pattern containment, permutations, layered permutations, packing density

References:

1. M.H. Albert, M.D. Atkinson, C.C. Handley, D.A. Holton, and W. Stromquist, On packing densities of permutations, Elect. J. Combin. 9 (2002) #R5.

2. M. Bóna, Combinatorics of Permutations, CRC Press, 2004.

3. P.A.Hästö, The packing density of other layered permutations, Elect. J. Combin. 9 (2) (2002) #R1.

4. M. Hildebrand, B.E. Sagan, and V.R. Vatter, Bounding quantities related to the packing density of 1(ℓ+1)ℓ …2, Adv. Appl. Math. 33 (2004) 633--653.

5. A. Price, Packing Densities of Layered Patterns, Ph. D. Thesis, University of Pennsylvania, 1997.