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

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.

Sources & referencesView supporting material

Primary source

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

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