S. V. Fomin, Nathan Lulov, “On the number of rim hook tableaux”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Zap. Nauchn. Sem. POMI, 223, POMI, St. Petersburg, 1995, 219–226; J. Math. Sci. (New York), 87:6 (1997), 4118

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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 223, Pages 219–226 (Mi znsl4388)

This article is cited in 16 scientific papers (total in 16 papers)

Combinatorial and algorithmic methods

On the number of rim hook tableaux

S. V. Fomin^a, Nathan Lulov^b

^a Department of Mathematics, St. Petersburg Institute of Informatics
^b Department of Mathematics, Harvard University

Full-text PDF (345 kB) Citations (16)

Abstract: A hooklength formula for the number of rim hook tableaux is used to obtain an inequality relating the number of rim hook tableaux of a given shape to the number of standard Young tableaux of the same shape. This provides an upper bound for a certain family of characters of the symmetric group. The analogues for shifted shapes and rooted trees are also given. Bibliography: 13 titles.

Received: 15.12.1994

English version:
Journal of Mathematical Sciences (New York), 1997, Volume 87, Issue 6, Pages 4118–4123
DOI: https://doi.org/10.1007/BF02355806

Bibliographic databases:

Document Type: Article

UDC: 519.117

Language: English

Citation: S. V. Fomin, Nathan Lulov, “On the number of rim hook tableaux”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Zap. Nauchn. Sem. POMI, 223, POMI, St. Petersburg, 1995, 219–226; J. Math. Sci. (New York), 87:6 (1997), 4118–4123

Citation in format AMSBIB

\Bibitem{FomLul95}

\by S.~V.~Fomin, Nathan~Lulov

\paper On the number of rim hook tableaux

\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~I

\serial Zap. Nauchn. Sem. POMI

\yr 1995

\vol 223

\pages 219--226

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl4388}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1374321}

\zmath{https://zbmath.org/?q=an:0909.05046|0884.05095}

\transl

\jour J. Math. Sci. (New York)

\yr 1997

\vol 87

\issue 6

\pages 4118--4123

\crossref{https://doi.org/10.1007/BF02355806}

Linking options:

https://www.mathnet.ru/eng/znsl4388

https://www.mathnet.ru/eng/znsl/v223/p219

This publication is cited in the following 16 articles:

Nanying Yang, Alexey M. Staroletov, “The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups”, J. Algebra Appl., 20:11 (2021)
Chaim Even-Zohar, Michael Farber, “Random Surfaces with Boundary”, Discrete Comput Geom, 66:4 (2021), 1463
Per Alexandersson, Stephan Pfannerer, Martin Rubey, Joakim Uhlin, “Skew characters and cyclic sieving”, Forum of Mathematics, Sigma, 9 (2021)
Philip Engel, “Hurwitz theory of elliptic orbifolds, I”, Geom. Topol., 25:1 (2021), 229
Bhargavi Jonnadula, Jonathan P. Keating, Francesco Mezzadri, “Symmetric function theory and unitary invariant ensembles”, Journal of Mathematical Physics, 62:9 (2021)
Sergei Chmutov, Boris Pittel, “On a surface formed by randomly gluing together polygonal discs”, Advances in Applied Mathematics, 73 (2016), 23
Purbhoo K., “Wronskians, Cyclic Group Actions, and Ribbon Tableaux”, Trans. Am. Math. Soc., 365:4 (2013), 1977–2030
Aner Shalev, Bolyai Society Mathematical Studies, 25, Erdős Centennial, 2013, 611
Belolipetsky M., Gelander Ts., Lubotzky A., Shalev A., “Counting Arithmetic Lattices and Surfaces”, Ann. Math., 172:3 (2010), 2197–2221
Larsen M., Shalev A., “Characters of Symmetric Groups: Sharp Bounds and Applications”, Invent. Math., 174:3 (2008), 645–687
Thomas W. Müller, Jan-Christoph Schlage-Puchta, “Character theory of symmetric groups, subgroup growth of Fuchsian groups, and random walks”, Advances in Mathematics, 213:2 (2007), 919
Alex Gamburd, “Poisson–Dirichlet distribution for random Belyi surfaces”, Ann. Probab., 34:5 (2006)
Aner Shalev, Progress in Mathematics, 248, Infinite Groups: Geometric, Combinatorial and Dynamical Aspects, 2005, 363
Martin W. Liebeck, Aner Shalev, “Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks”, Journal of Algebra, 276:2 (2004), 552
Lulov N., Pak I., “Rapidly Mixing Random Walks and Bounds on Characters of the Symmetric Group”, J. Algebr. Comb., 16:2 (2002), 151–163
Vishne U., “Mixing and Covering in the Symmetric Groups”, J. Algebra, 205:1 (1998), 119–140

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

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