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.
Citation: Shishuo Fu, Jiaxi Lu, Yuanzhe Ding. A skeleton model to enumerate standard puzzle sequences[J]. Electronic Research Archive, 2022, 30(1): 179-203. doi: 10.3934/era.2022010
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.
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Shishuo Fu, Jiaxi Lu, Yuanzhe Ding. A skeleton model to enumerate standard puzzle sequences[J]. Electronic Research Archive, 2022, 30(1): 179-203. doi: 10.3934/era.2022010
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