Bounding quantities related to the packing density of 1 (ℓ+1 )ℓ… 2
With Martin Hildebrand and Bruce Sagan.
Advances in Applied Mathematics, 33 (2004), 633-653. doi:10.1016/j.aam.2004.01.002.
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.
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Related links:
- This work is briefly covered in the notes for a talk I gave at the Rutgers Graduate Student Combinatorics Seminar, which are available in pdf, ps, or tex.
- The sequence Mn for the pattern 132 is number A061061 in the OEIS.
- The sequence Mn for the pattern 1432 is number A100354 in the OEIS.
- The sequence Mn for the pattern 15432 is number A100355 in the OEIS.
- The sequence Mn for the pattern 165432 is number A100356 in the OEIS.