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Mosc. Math. J., 2006, Volume 6, Number 3, Pages 461–475 (Mi mmj256)  

This article is cited in 13 scientific papers (total in 13 papers)

The boundary of the Eulerian number triangle

A. V. Gnedina, G. I. Olshanskiib

a Utrecht University
b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: The Eulerian triangle is a classical array of combinatorial numbers defined by a linear recursion. The associated boundary problem asks one to find all extreme nonnegative solutions to a dual recursion. Exploiting connections with random permutations and Markov chains we show that the boundary is discrete and explicitly identify its elements.

Key words and phrases: Eulerian numbers, extreme boundary, descents.

DOI: https://doi.org/10.17323/1609-4514-2006-6-3-461-475

Full text: http://www.ams.org/.../abst6-3-2006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 60J50, 60C05
Received: March 6, 2006
Language:

Citation: A. V. Gnedin, G. I. Olshanskii, “The boundary of the Eulerian number triangle”, Mosc. Math. J., 6:3 (2006), 461–475

Citation in format AMSBIB
\Bibitem{GneOls06}
\by A.~V.~Gnedin, G.~I.~Olshanskii
\paper The boundary of the Eulerian number triangle
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 3
\pages 461--475
\mathnet{http://mi.mathnet.ru/mmj256}
\crossref{https://doi.org/10.17323/1609-4514-2006-6-3-461-475}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2274860}
\zmath{https://zbmath.org/?q=an:1126.60065}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595900004}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gnedin A., Olshanski G., “A $q$-analogue of de Finetti's theorem”, Electron. J. Combin., 16:1 (2009), R78, 16 pp.  mathscinet  zmath  isi  elib
    2. Gnedin A., Olshanskii G., “$q$-exchangeability via quasi-invariance”, Ann. Probab., 38:6 (2010), 2103–2135  crossref  mathscinet  zmath  isi  elib  scopus
    3. Frick S.B., Petersen K., “Reinforced Random Walks and Adic Transformations”, J. Theoret. Probab.Reinforced random walks and adic transformations, 23:3 (2010), 920–943  crossref  mathscinet  zmath  isi  scopus
    4. Petersen K., Varchenko A., “The Euler Adic Dynamical System and Path Counts in the Euler Graph”, Tokyo J. Math., 33:2 (2010), 327–340  crossref  mathscinet  zmath  isi  scopus
    5. Strasser G., “Generalisations of the Euler adic”, Math. Proc. Cambridge Philos. Soc., 150:2 (2011), 241–256  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Gnedin A., “Coherent random permutations with biased record statistics”, Discrete Math., 311:1 (2011), 80–91  crossref  mathscinet  zmath  isi  elib  scopus
    7. Gnedin A., “Boundaries From Inhomogeneous Bernoulli Trials”, Random Walks, Boundaries and Spectra, Progress in Probability, 64, eds. Lenz D., Sobieczky F., Woess W., Birkhauser Verlag Ag, 2011, 91–110  mathscinet  zmath  isi
    8. Evans S.N., Gruebel R., Wakolbinger A., “Trickle-down processes and their boundaries”, Electron J Probab, 17 (2012), 1  crossref  mathscinet  zmath  isi  elib  scopus
    9. Hauser H., Koutschan Ch., “Multivariate Linear Recurrences and Power Series Division”, Discrete Math., 312:24 (2012), 3553–3560  crossref  mathscinet  zmath  isi  scopus
    10. Petersen K., Varchenko A., “Path Count Asymptotics and Stirling Numbers”, Proc. Amer. Math. Soc., 140:6 (2012), 1909–1919  crossref  mathscinet  zmath  isi  scopus
    11. Gnedin A., Gorin V., Kerov S., “Block Characters of the Symmetric Groups”, J. Algebr. Comb., 38:1 (2013), 79–101  crossref  mathscinet  zmath  isi  elib  scopus
    12. Janvresse E., Laurent S., de la Rue T., “Standardness of Monotonic Markov Filtrations”, Markov Process. Relat. Fields, 22:4 (2016), 697–736  mathscinet  zmath  isi
    13. Gnedin A., Gorin V., “Spherically Symmetric Random Permutations”, Random Struct. Algorithms, 55:2 (2019), 342–355  crossref  mathscinet  zmath  isi  scopus
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