Bijective Combinatorics of Young Tableaux

年轻画面的双射组合

• 批准号: 1001842
• 负责人: Igor Pak
• 金额: $ 27万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1001842&HistoricalAwards=false
• 关键词: Bijective; Combinatorics; Young; Tableaux

In the past few years there has been a growing number of connections between enumerative algebraic geometry, in particularly Gromov-Witten theory, and the algebraic combinatorics, in particular Young tableaux identities. The proposer intend to pursue the study of combinatorial bijections related to these identities. In particular, he intends to investigate multi-weighted analogues of certain classical combinatorial identities which also arise naturally from the representation theory of the symmetric group. He also intends to pursue both enumerative, algebraic and probabilistic applications of the discrete random processes for generation of weighted Young tableaux.Young tableaux are basic combinatorial structure which were introduced over a hundred years ago in connection with studies of a large class of spaces with symmetries. Over the years, Young tableaux have been further studied in connection with other fields of studies, such as statistical physics, discrete probability, and more recently, algebraic geometry and field theory. The reviewer intends to pursue the combinatorial aspects of the latter connections, with the intension of developing new tools, which in turn will lead to new results in both fields.

在过去的几年里，枚举代数几何（特别是格罗莫夫-维滕理论）与代数组合学（特别是杨格恒等式）之间的联系越来越多。 提议者打算继续研究与这些恒等式相关的组合双射。特别是，他打算研究某些经典组合恒等式的多权类似物，这些类似物也是从对称群的表示论中自然产生的。他还打算追求离散随机过程的枚举、代数和概率应用，以生成加权 Young 画面。Young 画面是一百多年前在对一大类对称空间的研究中引入的基本组合结构。 。多年来，杨氏造型与其他研究领域相结合得到了进一步研究，例如统计物理学、离散概率，以及最近的代数几何和场论。 审稿人打算追求后一种联系的组合方面，意图开发新工具，这反过来将在这两个领域带来新的结果。