Conjecture on the distribution for 021-avoiding ascent sequences
Conjecture on the distribution for 021-avoiding ascent sequences
Let be the set of ascent sequences of length avoiding , and let and denote, respectively, the number of ascents and right-to-left minima. The 021 bistatistic conjecture. The bistatistic has the same distribution on as on the 132-avoiding permutations of length . The source subsequently reports that Bruce Sagan proved this conjecture in personal communication.
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Primary source
Paul Duncan and Einar Steingrimsson, “Pattern avoidance in ascent sequences”, arXiv:1109.3641 (2011).
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