On minimal pattern-containing inversion sequences
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910035130449920 |
|---|---|
| author | Testart, Benjamin |
| author_facet | Testart, Benjamin |
| contents | We introduce the notion of minimal inversion sequences for a pattern $ρ$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $ρ$ for inversion sequences. We give a characterization of $ρ$-minimal inversion sequences based on the occurrences of the pattern $ρ$ they contain, and use it to find upper and lower bounds on the lengths of $ρ$-minimal inversion sequences. We provide some enumerative results on the exact number of minimal inversion sequences for some patterns, through a bijection with increasing trees, and some exhaustive generation. Lastly, we enumerate inversion sequences which are equal to their reduction, and find an interesting connection with poly-Bernoulli numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On minimal pattern-containing inversion sequences Testart, Benjamin Combinatorics We introduce the notion of minimal inversion sequences for a pattern $ρ$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $ρ$ for inversion sequences. We give a characterization of $ρ$-minimal inversion sequences based on the occurrences of the pattern $ρ$ they contain, and use it to find upper and lower bounds on the lengths of $ρ$-minimal inversion sequences. We provide some enumerative results on the exact number of minimal inversion sequences for some patterns, through a bijection with increasing trees, and some exhaustive generation. Lastly, we enumerate inversion sequences which are equal to their reduction, and find an interesting connection with poly-Bernoulli numbers. |
| title | On minimal pattern-containing inversion sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.12130 |