分拆统计量研究中的构造性方法

整数分拆理论是同属于组合数学和数论的一个交叉研究领域，该领域的主要研究方法分为代数方法和组合方法。其中组合方法因其优美的构造方式及简洁的证明过程受到学者们的关注。特别的，构造统计量和映射研究分拆及限制分拆函数的算术性质吸引了包括英国皇家数学学会会员F.J.Dyson，美国科学院院士G.E.Andrews以及佛罗里达大学组合学家F.G.Garvan在内的众多学者，是一个非常活跃的研究方向。.本项目围绕分拆统计量的组合构造展开，探索统计量研究中的构造性方法，主要研究内容包括：限制分拆函数算术性质的双射证明、分拆（限制分拆）函数同余性质的细化以及分拆统计量序列的单峰性。

The theory of integer partition is an interdisciplinary research area of combinatorics and number theory. Studies on the theory of integer partition usually adopt algebraic and combinatorial methods, of which the latter attracts significant attention from many scholars given its beautiful construction. In particular, investigating the arithmetic properties for partition (restricted partition) functions by constructing statistics and bijections has attracted the attention of researchers including the Royal Mathematical Society member F.J.Dyson, the National Academy of Sciences fellow G.E.Andrews and the professor of the University of Florida F.G.Garvan..This project will focus on the combinatorial construction of statistics on integer partitions investigating the constructive methods in the following aspects: bijective proofs of arithmetic properties for restricted partition functions; refinements of congruences for partition (restricted partition) functions; the unimodality properties on statistics.