Open AccessA skeleton model to enumerate standard puzzle sequences
Author(s) -
Shishuo Fu,
AUTHOR_ID,
Lu Jia-Xi,
Yuanzhe Ding,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022010
Subject(s) - enumeration , skeleton (computer programming) , mathematics , combinatorics , catalan number , object (grammar) , standard model (mathematical formulation) , sequence (biology) , discrete mathematics , arithmetic , computer science , artificial intelligence , programming language , biology , history , genetics , archaeology , gauge (firearms)
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.