AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Electronic Research Archive Article
PDF (732.8 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

A skeleton model to enumerate standard puzzle sequences

Shishuo Fu1, Jiaxi Lu1( ), Yuanzhe Ding2
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Hongshen Honors School, Chongqing University, Chongqing 401331, China
Show Author Information

Abstract

Guo-Niu Han [Sémin. Lothar. Comb. 85 (2021) B85c (electronic)] has introduced a new combinatorial object named standard puzzle. We use digraphs to show the relations between numbers in standard puzzles and propose a skeleton model. By this model, we solve the enumeration problem of over fifty thousand standard puzzle sequences. Most of them can be represented by classical numbers, such as Catalan numbers, double factorials, secant numbers and so on. Also, we prove several identities for standard puzzle sequences.

Keywords

standard puzzleenumerationbijective combinatoricssecant numberCatalan numberdouble factorialhypergeometric series

References

【1】
【1】
 
 
Crossref Google Scholar
Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 179-203
DOI: 10.3934/era.2022010

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Fu S, Lu J, Ding Y. A skeleton model to enumerate standard puzzle sequences. Electronic Research Archive, 2022, 30(1): 179-203. https://doi.org/10.3934/era.2022010

3

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 15 July 2021
Revised: 10 November 2021
Accepted: 12 November 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)