Enumerating k-connected blocks and gk-connected blocks in words
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915203110666240 |
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| author | Asakly, Walaa Kezil, Noor |
| author_facet | Asakly, Walaa Kezil, Noor |
| contents | We define two new statistics on words: the k-connector and the gk-connector. For a word $π= π_1π_2\cdotsπ_n$ of length $n$ over the alphabet $[k]$, a k-connector is defined as an ordered pair $(π_j, π_{j+1})$ where $1 \leq j \leq n-1$ and $π_j + π_{j+1} = k$. Conversely, a gk-connector is defined as an ordered pair $(π_j, π_{j+1})$ where $1 \leq j \leq n-1$ and $π_j + π_{j+1} > k$. We investigate the enumeration of partitions based on these statistics, providing generating functions and explicit formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumerating k-connected blocks and gk-connected blocks in words Asakly, Walaa Kezil, Noor Combinatorics We define two new statistics on words: the k-connector and the gk-connector. For a word $π= π_1π_2\cdotsπ_n$ of length $n$ over the alphabet $[k]$, a k-connector is defined as an ordered pair $(π_j, π_{j+1})$ where $1 \leq j \leq n-1$ and $π_j + π_{j+1} = k$. Conversely, a gk-connector is defined as an ordered pair $(π_j, π_{j+1})$ where $1 \leq j \leq n-1$ and $π_j + π_{j+1} > k$. We investigate the enumeration of partitions based on these statistics, providing generating functions and explicit formulas. |
| title | Enumerating k-connected blocks and gk-connected blocks in words |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.14073 |