A skeleton model to enumerate standard puzzle sequences

TL;DR

This paper introduces a skeleton model for standard puzzles, enabling the enumeration of over fifty thousand sequences and revealing connections to classical combinatorial numbers.

Contribution

It proposes a novel skeleton model for standard puzzles and solves the enumeration problem for a large class of sequences, linking them to known combinatorial numbers.

Findings

Enumerated over 50,000 standard puzzle sequences.

Most sequences relate to classical numbers like Catalan and Secant numbers.

Proved several identities within standard puzzle sequences.

Abstract

Guo-Niu Han [arXiv:2006.14070 [math.CO]] 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 in standard puzzle sequences.