We bound several quantities related to the packing density of the patterns 1(ℓ+1)ℓ⋯2. These bounds sharpen results of Bóna, Sagan, and Vatter and give a new proof of the packing density of these patterns, originally computed by Stromquist in the case ℓ=2 and by Price for larger ℓ. We end with comments and conjectures. © 2004 Elsevier Inc. All rights reserved.
Hildebrand, M., Sagan, B. E., & Vatter, V. R. (2004). Bounding quantities related to the packing density of 1(ℓ+1)ℓ⋯2. Advances in Applied Mathematics, 33(3), 633–653. https://doi.org/10.1016/j.aam.2004.01.002