کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4655293 | 1632945 | 2014 | 43 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A diagrammatic approach to Kronecker squares
ترجمه فارسی عنوان
رویکرد نمودار به مربع کرونکر
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
In this paper we improve a method of Robinson and Taulbee for computing Kronecker coefficients and show that for any partition ν¯ of d there is a polynomial kν¯ with rational coefficients in variables xC, where C runs over the set of isomorphism classes of connected skew diagrams of size at most d, such that for all partitions λ of n, the Kronecker coefficient g(λ,λ,(nâd,ν¯)) is obtained from kν¯(xC) substituting each xC by the number of partitions α contained in λ such that λ/α is in the class C. Some results of our method extend to arbitrary Kronecker coefficients. We present two applications. The first is a contribution to the Saxl conjecture, which asserts that if Ïk=(k,kâ1,â¦,2,1) is the staircase partition, then the Kronecker square ÏÏâÏÏ contains every irreducible character of the symmetric group as a component. Here we prove that for any partition ν¯ of size d there is a piecewise polynomial function sν¯ in one real variable such that for all k, one has g(Ïk,Ïk,(|Ïk|âd,ν¯))=sν¯(k). The second application is a proof of a new stability property for arbitrary Kronecker coefficients.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 127, September 2014, Pages 243-285
Journal: Journal of Combinatorial Theory, Series A - Volume 127, September 2014, Pages 243-285
نویسندگان
Ernesto Vallejo,