Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams

By Alexander V. Gnedin, Grigori Olshanski. 2005

50 citations recorded by the source corpus.

The graph of zigzag diagrams is a close relative of Young's lattice. The boundary problem for this graph amounts to describing coherent random permutations with descent-set statistic, and is also related to certain positive characters on the algebra of quasi-symmetric functions. We establish connections to some further relatives of Young's lattice and solve the boundary problem by reducing it to the classification of spreadable total orders on integers, as recently obtained by Jacka and Warren.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cabd8d39898d8e1f43bf656a305d7fd3b08c6ca8

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Citations in the corpus

Modules of the 0-Hecke algebra and quasisymmetric Schur functions (2014, background): “They have also been seen to simplify many symmetric functions such as Macdonald polynomials [26, 27], Kazhdan-Lusztig polynomials [8] and identify equal ribbon Schur functions [10], as well as arising in category theory [2], topology [4, 25], and graph theory [15, 32, 51].”
Representations of the Infinite Symmetric Group (2016, methodology): “Our exposition is based on the works of Olshanski [87] and Kerov, Olshanski, and Vershik [67].”