Conjecture on Supersequence Lower Bound related to Connell Sequence
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909461282553856 |
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| author | Tan, Oliver |
| author_facet | Tan, Oliver |
| contents | This paper proves the minimum size of a supersequence over a set of eight elements is 52. This disproves a conjecture that the lower bound of the supersequence is the partial sum of the geometric Connell sequence. By studying the internal distribution of individual elements within sub-strings of the supersequence called segments, the proof provides important results on the internal structure that could help to understand the general lower bound problem for finite sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11386 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjecture on Supersequence Lower Bound related to Connell Sequence Tan, Oliver Combinatorics Discrete Mathematics 05A05, 05A15 This paper proves the minimum size of a supersequence over a set of eight elements is 52. This disproves a conjecture that the lower bound of the supersequence is the partial sum of the geometric Connell sequence. By studying the internal distribution of individual elements within sub-strings of the supersequence called segments, the proof provides important results on the internal structure that could help to understand the general lower bound problem for finite sets. |
| title | Conjecture on Supersequence Lower Bound related to Connell Sequence |
| topic | Combinatorics Discrete Mathematics 05A05, 05A15 |
| url | https://arxiv.org/abs/2501.11386 |