A Relation Between Schröder Paths and Motzkin Paths
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DOI: 10.1007/s00373-020-02185-6
Abstract: A small q -Schröder path of semilength n is a lattice path from (0, 0) to (2 n , 0) using up steps $$U = (1, 1)$$ U = ( 1 , 1 ) , horizontal steps… read more here.
Keywords: motzkin paths; der paths; small schr; schr der ... See more keywords
Involutions under Bruhat order and labeled Motzkin paths
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DOI: 10.1016/j.ejc.2022.103513
Abstract: In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by P. Biane from permutations to certain… read more here.
Keywords: motzkin paths; involutions bruhat; bruhat order; order labeled ... See more keywords
Limits of Random Motzkin Paths with KPZ Related Asymptotics
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DOI: 10.1093/imrn/rnaf022
Abstract: We study Motzkin paths of length $L$ with general weights on the edges and endpoints. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair… read more here.
Keywords: random motzkin; motzkin paths; related asymptotics; kpz related ... See more keywords