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

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

2005-08-07

arxiv.org/abs/math/0508131v2

Intern. Math. Research Notices 2006, Art. ID 51968, 39 pp.

Mathematics

Combinatorics

Version 2: more detailed exposition, 4 references added, page format changed, 44 pp.; accepted in IMRN

Scientific paper

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.

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