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The combinatorial community is awesome! On 6 Jan 2021, me and Jean-Luc Baril, we submitted to arXiv a paper about a [transformation à la Foata for special kinds of descents and excedances in permutattions](https://arxiv.org/abs/2103.13092). At the end of this paper we present two conjectures that straighten our result. On March 24, 2021, Bin Han, Jianxi Mao, Jiang Zeng anounced the proof of our second conjecture. The paper above presents their work. The first conjecture remains open.
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Algorithm 1 makes me think of Algorithm 3 [here](https://www-complexnetworks.lip6.fr/~latapy/Publis/triangles_short.pdf)
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I wonder if we can obtain asymptotic results in the same manner...
A related [question](https://mathoverflow.net/questions/384683/random-permutations-without-double-rises-avoiding-consecutive-pattern-underli/384947#384947) on Mathoverflow.
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Nice paper! Very clear and useful!! I do not see absolute time values in the experiments, just speedups. It would have been nice to show some absolute values too. I've implemented the algorithms [here](https://github.com/maxdan94/ParallelUnionFind). On a very large graphs with more than 10 billions of edges (the twitter graph [here](https://sites.google.com/view/limass/datasets)), I observe that the verification algorithm is faster and leads to better speedups than the lock algorithm.
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