论文标题
换档树木和Rogers-Ramanujan Identitits
Shift-Plethystic Trees and Rogers-Ramanujan Identitites
论文作者
论文摘要
通过在无限字母中研究非交流性序列，我们引入了换档树木和一类整数组成，作为罗杰斯 - 拉曼努扬身份的新组合模型。我们证明，与移位树木相关的语言可以表示为Rogers-Ramanujan的非共同概括，继续分数。通过将非交通性系列专门为$ q $系列，我们可以根据签名的整数组成来为Rogers-Ramanujan身份获得新的组合解释。我们介绍了在非交通序列上的Shift-plethysm的操作，并使用它来获得有趣的枚举身份，这些身份涉及与Rogers-Ramanujan身份相关的组成和分区。
By studying non-commutative series in an infinite alphabet we introduce shift-plethystic trees and a class of integer compositions as new combinatorial models for the Rogers-Ramanujan identities. We prove that the language associated to shift-plethystic trees can be expressed as a non-commutative generalization of the Rogers-Ramanujan continued fraction. By specializing the noncommutative series to $q$-series we obtain new combinatorial interpretations to the Rogers-Ramanujan identities in terms of signed integer compositions. We introduce the operation of shift-plethysm on non-commutative series and use this to obtain interesting enumerative identities involving compositions and partitions related to Rogers-Ramanujan identities.
