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arXiv · 2603.17287

Forest webs and pattern avoidance

Jessica Striker·Bridget Eileen Tenner
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Abstract

In a recent preprint, Mike Cummings showed that the smooth components of suitably parametrized Springer fibers are in bijection with contracted, fully reduced Pl\"ucker degree-two $\mathfrak{sl}_r$-webs of standard type and that are forests. He showed these are enumerated by sequence A116731 in the OEIS, which is equinumerous with permutations avoiding the patterns {321,2143,3124}. Cummings posed the problem of strengthening this enumerative result by finding a bijection between these webs and a collection of pattern-avoiding permutations. Here we solve this problem, although notably not with the collection of patterns that Cummings had proposed. Rather, we give a bijection between this class of webs and permutations avoiding the patterns {132,4321,3214}.

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Jessica Striker, Bridget Eileen Tenner. 2026-03-18. Forest webs and pattern avoidance. https://arxiv.org/abs/2603.17287

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