Quasi-symmetric functions as polynomial functions on Young diagrams

被引：4

作者：

Aval, Jean-Christophe ^{[1
]}

Feray, Valentin ^{[2
]}

Novelli, Jean-Christophe ^{[3
]}

Thibon, Jean-Yves ^{[3
]}

机构：

[1] Univ Bordeaux 1, LaBRI, F-33405 Talence, France

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[3] Univ Paris Est Marne La Vallee, Inst Gaspard Monge, F-77454 Marne La Vallee 2, France

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2015年 / 41卷 / 03期

关键词：

Quasi-symmetric functions; Functions on Young diagrams; Evaluation on virtual alphabets; COMBINATORIAL INTERPRETATION; CHARACTERS;

D O I：

10.1007/s10801-014-0549-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the shape of the diagram. We prove that the algebra of such functions is isomorphic to quasi-symmetric functions, and give a noncommutative analog of this result.

引用

页码：669 / 706

页数：38