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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Path count asymptotics and Stirling numbers


Authors: K. Petersen and A. Varchenko
Journal: Proc. Amer. Math. Soc. 140 (2012), 1909-1919
MSC (2010): Primary 05A10, 05A16, 05A19, 05C30, 05C63; Secondary 37A05, 37A50
Published electronically: October 12, 2011
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Abstract: We obtain formulas for the growth rate of the numbers of certain paths in a multi-dimensional analogue of the Eulerian graph. Corollaries are new identities relating Stirling numbers of the first and second kinds.


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Additional Information

K. Petersen
Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250
Email: petersen@math.unc.edu

A. Varchenko
Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250
Email: anv@math.unc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11052-9
PII: S 0002-9939(2011)11052-9
Keywords: Eulerian numbers, Stirling numbers, symmetric polynomials, reinforced random walks, urn models
Received by editor(s): December 8, 2009
Received by editor(s) in revised form: February 7, 2011
Published electronically: October 12, 2011
Additional Notes: The research of the second author was supported in part by NSF grant DMS-0555327
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society