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 Zap. Nauchn. Sem. POMI, 2004, Volume 307, Pages 266–280 (Mi znsl847)

On the coincidence of limit shapes for integer partitions and compositions, and a slicing of Young diagrams

Yu. V. Yakubovich

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We consider a slicing of Young diagrams into slices associated with summands that have equal multiplicities. It is shown that for the uniform measure on all partitions of an integer $n$, as well as for the uniform measure on partitions of an integer $n$ into $m$ summands, $m\sim An^\alpha$, $\alpha\le1/2$, all slices after rescaling concentrate around their limit shapes. The similar problem is solved for compositions of an integer $n$ into $m$ summands. These results are applied to explain why limit shapes of partitions and compositions coincide in the case $\alpha<1/2$.

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English version:
Journal of Mathematical Sciences (New York), 2005, 131:2, 5569–5577

Bibliographic databases:

UDC: 519.2

Citation: Yu. V. Yakubovich, “On the coincidence of limit shapes for integer partitions and compositions, and a slicing of Young diagrams”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Zap. Nauchn. Sem. POMI, 307, POMI, St. Petersburg, 2004, 266–280; J. Math. Sci. (N. Y.), 131:2 (2005), 5569–5577

Citation in format AMSBIB
\Bibitem{Yak04} \by Yu.~V.~Yakubovich \paper On the coincidence of limit shapes for integer partitions and compositions, and a~slicing of Young diagrams \inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~X \serial Zap. Nauchn. Sem. POMI \yr 2004 \vol 307 \pages 266--280 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl847} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2050695} \zmath{https://zbmath.org/?q=an:1162.11385} \elib{http://elibrary.ru/item.asp?id=9127655} \transl \jour J. Math. Sci. (N. Y.) \yr 2005 \vol 131 \issue 2 \pages 5569--5577 \crossref{https://doi.org/10.1007/s10958-005-0427-1} \elib{http://elibrary.ru/item.asp?id=13492543}