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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.18626 |
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| _version_ | 1866910149813207040 |
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| author | Yi, Kai |
| author_facet | Yi, Kai |
| contents | Defant and Zheng introduced a consecutive-pattern-avoiding stack sort map $SC_σ$, where the stack must avoid a consecutive pattern $σ$. Seidel and Sun disproved a conjecture in Defant and Zheng's paper about the maximum sort-number of a length $n$ permutation under $SC_{231}$. In this paper, we compute sort-numbers for each permutation of length up to $14$, and we estimate the average sort-numbers up to length $1000$. Our results suggest the maximum and average sort-numbers grow faster than linear with respect to $n$ for the tested ranges, though the long-term behavior remains unclear. We also prove properties of $SC_{231}$ mathematically, such as a $n-1$ lower bound and a $\frac{(n+1)(n-2)}{2}$ upper bound for the maximum sort-number of length $n$ permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computational Approach to the $SC_{231}$ Consecutive-Pattern-Avoiding Stack Sort Yi, Kai Combinatorics Defant and Zheng introduced a consecutive-pattern-avoiding stack sort map $SC_σ$, where the stack must avoid a consecutive pattern $σ$. Seidel and Sun disproved a conjecture in Defant and Zheng's paper about the maximum sort-number of a length $n$ permutation under $SC_{231}$. In this paper, we compute sort-numbers for each permutation of length up to $14$, and we estimate the average sort-numbers up to length $1000$. Our results suggest the maximum and average sort-numbers grow faster than linear with respect to $n$ for the tested ranges, though the long-term behavior remains unclear. We also prove properties of $SC_{231}$ mathematically, such as a $n-1$ lower bound and a $\frac{(n+1)(n-2)}{2}$ upper bound for the maximum sort-number of length $n$ permutations. |
| title | Computational Approach to the $SC_{231}$ Consecutive-Pattern-Avoiding Stack Sort |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.18626 |