298 research outputs found

    Enumeration of Standard Young Tableaux

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    A survey paper, to appear as a chapter in a forthcoming Handbook on Enumeration.Comment: 65 pages, small correction

    The oriented swap process and last passage percolation

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    We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process on nn particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic identities, relating a random vector of last passage percolation times to its dual, using the duality between the Robinson-Schensted-Knuth and Burge correspondences. A second probabilistic identity, relating those two vectors to a vector of 'last swap times' in the oriented swap process, is conjectural. We give a computer-assisted proof of this identity for n≤6n\le 6 after first reformulating it as a purely combinatorial identity, and discuss its relation to the Edelman-Greene correspondence. The conjectural identity provides precise finite-nn and asymptotic predictions on the distribution of the absorbing time of the oriented swap process, thus conditionally solving an open problem posed by Angel, Holroyd and Romik.Comment: 36 pages, 6 figures. Full version of the FPSAC 2020 extended abstract arXiv:2003.0333
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