Fu and Lin's four-statistic equidistribution conjecture for 2314-avoiding permutations

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Let cmathfrakSn(23‾14)cmathfrak{S}_n(\underline{23}14) be the permutations avoiding the vincular pattern 23‾14\underline{23}14, and let cmathbfIn(110)cmathbf{I}_n(110) be the inversion sequences avoiding 110110. For a permutation cmathitπcmathit{\pi}, let cmathrmrmincmathrm{rmin}, cmathrmlmincmathrm{lmin} and cmathrmrmaxcmathrm{rmax} denote the numbers of right-to-left minima, left-to-right minima and right-to-left maxima, respectively, and let cmathrmasccmathrm{asc} denote the number of ascents. For an inversion sequence ee, let cmathrmzero(e)cmathrm{zero}(e) be the number of zero entries, cmathrmmax⁡(e)=∣{i∈[n]:ei=i−1}∣cmathrm{\max}(e)=|\{i\in[n]:e_i=i-1\}|, and cmathrmrep(e)=n−∣{e1,e2,…,en}∣cmathrm{rep}(e)=n-|\{e_1,e_2,\ldots,e_n\}|. Fu and Lin's equidistribution conjecture. The quadruple (rmin⁡,lmin⁡,rmax⁡,asc⁡)(\operatorname{rmin},\operatorname{lmin},\operatorname{rmax},\operatorname{asc}) on cmathfrakSn(23‾14)cmathfrak{S}_n(\underline{23}14) has the same distribution as (zero⁡,max⁡,rmin⁡,rep⁡)(\operatorname{zero},\operatorname{max},\operatorname{rmin},\operatorname{rep}) on cmathbfIn(110)cmathbf{I}_n(110). The conjecture was verified computationally for 1≤n≤91\leq n\leq9 and refines the proposed equidistribution between statistics on vincular pattern-avoiding permutations and inversion sequences.

References

Primary source

Zhicong Lin and Shishuo Fu, “On 120-avoiding inversion and ascent sequences”, arXiv:2003.11813 (2020).

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