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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Schröder’s problems and scaling limits of random trees
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by Jim Pitman and Douglas Rizzolo PDF
Trans. Amer. Math. Soc. 367 (2015), 6943-6969 Request permission

Abstract:

In his now classic paper of 1870, Schröder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on average. For each of the four problems we prove that a uniform pick from the appropriate set of bracketings, when considered as a tree, has the Brownian continuum random tree as its scaling limit as the size of the word or set goes to infinity.
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Additional Information
  • Jim Pitman
  • Affiliation: Department of Statistics, University of California, Berkeley, California 94720
  • MR Author ID: 140080
  • Email: pitman@stat.berkeley.edu
  • Douglas Rizzolo
  • Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98105
  • MR Author ID: 814330
  • Email: drizzolo@math.washington.edu
  • Received by editor(s): April 5, 2013
  • Received by editor(s) in revised form: June 12, 2013
  • Published electronically: January 15, 2015
  • Additional Notes: The first author was supported in part by NSF Grant No. 0806118
    The second author was supported in part by NSF Grant No. 0806118, in part by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1106400, and in part by NSF DMS-1204840.
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 6943-6969
  • MSC (2010): Primary 60C05, 60J80
  • DOI: https://doi.org/10.1090/S0002-9947-2015-06254-0
  • MathSciNet review: 3378819