Combinatorial Generation Algorithms for Directed Lattice Paths

Author:

Shablya Yuriy1ORCID,Merinov Arsen1,Kruchinin Dmitry1ORCID

Affiliation:

1. Laboratory of Algorithms and Technologies for Discrete Structures Research, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia

Abstract

Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified properties. This article is devoted to issues related to the construction of such combinatorial generation algorithms for a wide class of directed lattice paths. The main method used is based on the representation of a given combinatorial set in the form of an AND/OR tree structure. To apply this method, it is necessary to have an expression for the cardinality function of a combinatorial set that satisfies certain requirements. As the main result, we have found recurrence relations for enumerating simple directed lattice paths that satisfy the requirements of the applied method and have constructed the corresponding AND/OR tree structure. Applying the constructed AND/OR tree structure, we have developed new algorithms for ranking and unranking simple directed lattice paths. Additionally, the obtained results were generalized to the case of directed lattice paths.

Funder

Russian Science Foundation

Publisher

MDPI AG

Reference39 articles.

1. A history and a survey of lattice path enumeration;Humphreys;J. Statist. Plann. Inference,2010

2. Stanley, R.P. (2012). Enumerative Combinatorics: Volume 1, Cambridge University Press. [2nd ed.].

3. Bona, M. (2015). Handbook of Enumerative Combinatorics, CRC Press.

4. Wallner, M. (2016). Combinatorics of Lattice Paths and Tree-Like Structures. [Ph.D. Thesis, Institute of Discrete Mathematics and Geometry, Vienna University of Technology].

5. Dyck path enumeration;Deutsch;Discret. Math.,1999

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3