Geodesic
Modified ascent sequences and Bell numbers
Giulio Cerbai1
1University of Iceland
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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In 2011, Duncan and Steingrímsson conjectured that modified ascent sequences avoiding any of the patterns 212, 1212, 2132, 2213, 2231 and 2321 are counted by the Bell numbers. Furthermore, the distribution of the number of ascents is the reverse of the distribution of blocks on set partitions. We solve the conjecture for all the patterns except 2321. We describe the corresponding sets of Fishburn permutations by pattern avoidance, and leave some open questions for future work.
DOI : 10.37236/12080
Classification : 05A05, 05A19, 11B73
Mots-clés : Fishburn permutations, pattern avoidance, Bell numbers

Giulio Cerbai  1

1 University of Iceland 
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Giulio Cerbai. Modified ascent sequences and Bell numbers. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12080

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