中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
首页 机构 成果 学者
  
  1. CAS IR Grid
  2. 数学与系统科学研究院
  3. 中国科学院数学与系统科学研究院
Dinv, area, and bounce for (k)over-right-arrow-Dyck paths

文献类型：期刊论文

作者Xin, Guoce1; Zhang, Yingrui2
刊名ADVANCES IN APPLIED MATHEMATICS
出版日期2023-02-01
卷号143页码:19
关键词q, t-Catalan numbers Sweep map (k)over-right-arrow-Dyck paths
ISSN号0196-8858
DOI10.1016/j.aam.2022.102455
英文摘要The well-known q, t-Catalan sequence has two combinatorial interpretations as weighted sums of ordinary Dyck paths: one is Haglund's area-bounce formula, and the other is Haiman's dinv-area formula. The zeta map was constructed to connect these two formulas: it is a bijection from ordinary Dyck paths to themselves, and it takes dinv to area, and area to bounce. Such a result was extended for k-Dyck paths by Loehr. The zeta map was extended by Armstrong-Loehr-Warrington for a very general class of paths. In this paper, weextend the dinv-area-bounce result for (k) over right arrow -Dyck paths by: i) giving a geometric construction for the bounce statistic of a k-Dyck path, which includes the k-Dyck paths and ordinary Dyck paths as special cases; ii) giving a geometric interpretation of the dinv statistic of a (k) over right arrow -Dyck path. Our bounce construction is inspired by Loehr's construction and Xin-Zhang's linear algorithm for inverting the sweep map on (k) over right arrow -Dyck paths. Our dinv interpretation is inspired by Garsia-Xin's visual proof of dinv-to-area result on rational Dyck paths. (c) 2022 Elsevier Inc. All rights reserved.
资助项目NSFC ; [11871067]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000882526400002
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60577]  
专题中国科学院数学与系统科学研究院
通讯作者Zhang, Yingrui
作者单位1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Xin, Guoce,Zhang, Yingrui. Dinv, area, and bounce for (k)over-right-arrow-Dyck paths[J]. ADVANCES IN APPLIED MATHEMATICS,2023,143:19.
APA Xin, Guoce,&Zhang, Yingrui.(2023).Dinv, area, and bounce for (k)over-right-arrow-Dyck paths.ADVANCES IN APPLIED MATHEMATICS,143,19.
MLA Xin, Guoce,et al."Dinv, area, and bounce for (k)over-right-arrow-Dyck paths".ADVANCES IN APPLIED MATHEMATICS 143(2023):19.

入库方式： OAI收割

来源：数学与系统科学研究院

浏览0
下载0
收藏0
其他版本

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。