On Some Problems Related to Differential-Difference Recurrences

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Project title

Code/計畫編號

MOST106-2115-M019-001

Translated Name/計畫中文名

與微分-差分型遞迴關係有關的問題的研究

Project Coordinator/計畫主持人

Hua-Huai Chern

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Computer Science and Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=12228555

Year

2017

Start date/計畫起

01-08-2017

Expected Completion/計畫迄

31-07-2018

Bugetid/研究經費

219千元

ResearchField/研究領域

數學

本次研究計畫旨在針對能將出現在如組合結構、统計力學等領域裡幾類型可透過如徽分-差分型遞回關係式Differential-Difference Recurrences (DDR)來描述的貴際間題'透過研究如何明確地或漸遑地求解'來對原間題尭成完整分析。以遠主題為研究轴心的理由，除了有對應如與只伽如讲S如 Tableaux相關等具體的應用間題外'還可對仍未解決的從係數數列函數的條件判斷是否存在著可發展成一般性的論述的可能性'予以遑一步地探討與分析。In this project, the author aims to study how to obtain the method for solving explicitly or asymptotically the following types of Differential-Difference Recurrences (DDR) that appear in combinatorial structures, statistical mechanics and other fields. Such types of recurrences can be used to serve as the key for resolving many practical problems, for example, those ones related and linked to the Random Staircase Tableaux. The author shall device an alternative method to complete the analysis on these problems. Also, it is worthy of the effort to investigate further and deliberately whether it is possible to develop a generalized approach for dealing with such kinds of recurrences.

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On Some Problems Related to Differential-Difference Recurrences

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