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Efficient counting of permutation patterns via double posets

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arxiv 2408.08293 v2 pith:S4FL6ITR submitted 2024-08-15 math.CO cs.DM

Joscha Diehl , Emanuele Verri This is my paper · ORCID
classification math.COcs.DM
keywords doubleposetscornertreecountingefficienteven-zoharleng
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Corner trees, introduced in "Even-Zohar and Leng, 2021, Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms", allow for the efficient counting of certain permutation patterns. Here we identify corner trees as a subset of finite (strict) double posets, which we term twin-tree double posets. They are contained in both twin double posets and tree double posets, giving candidate sets for generalizations of corner tree countings. We provide the generalization of an algorithm proposed by Even-Zohar/Leng to a class of tree double posets, thereby enlarging the space of permutations that can be counted in O(n^{5/3}).

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  1. Tensor-to-Tensor Models with Fast Iterated Sum Features

    cs.CV 2025-06 conditional novelty 6.0 of 10

    A corner-tree algorithm computes a large class of two-parameter iterated sums in linear time, enabling a cheap tensor-to-tensor neural layer that matches larger ResNets on CIFAR and works for texture anomaly detection.

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