Conjecture on the (asc⁡,RLmin⁡)(\operatorname{asc},\operatorname{RLmin}) distribution for 021-avoiding ascent sequences

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Let S021(n){\mathcal S}_{021}(n) be the set of ascent sequences of length nn avoiding 021021, and let asc⁡\operatorname{asc} and RLmin⁡\operatorname{RLmin} denote, respectively, the number of ascents and right-to-left minima. The 021 bistatistic conjecture. The bistatistic (asc⁡,RLmin⁡)(\operatorname{asc},\operatorname{RLmin}) has the same distribution on S021(n){\mathcal S}_{021}(n) as on the 132-avoiding permutations of length nn. The source subsequently reports that Bruce Sagan proved this conjecture in personal communication.

References

Primary source

Paul Duncan and Einar Steingrimsson, “Pattern avoidance in ascent sequences”, arXiv:1109.3641 (2011).

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