On the Coincidence of Limit Shapes for Integer Partitions and Compositions, and a Slicing of Young Diagrams

Autor:	Yu. V. Yakubovich
Rok vydání:	2005
Předmět:	Statistics and Probability Discrete mathematics Combinatorics Applied Mathematics General Mathematics Bibliography Limit (mathematics) Composition (combinatorics) Measure (mathematics) Slicing Coincidence Mathematics Integer (computer science)
Zdroj:	Journal of Mathematical Sciences. 131:5569-5577
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-005-0427-1
Popis:	We consider the 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 with m ∼ Anα, α ≤ 1/2, 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 explain why the limit shapes of partitions and compositions coincide in the case α < 1/2. Bibliography: 10 titles.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::49309ad10d054e29bee0c9d3c7fbcadc https://doi.org/10.1007/s10958-005-0427-1 Zobrazit plný text záznamu Plný text ve formátu PDF