2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71340We 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.20 pages, 1 figure, Latex, to be published in Advances in Applied Math., see related papers at http://www.math.msu.edu/~saganCombinatorics05A20 (Primary); O5D99, 05E99 (Secondary)text