Counting finite $O$-sequences of a given multiplicity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908948476461056 |
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| author | Cioffi, Francesca Guida, Margherita |
| author_facet | Cioffi, Francesca Guida, Margherita |
| contents | We study the number $O_d$ of finite $O$-sequences of a given multiplicity $d$, with particular attention to the computation of $O_d$. We show that the sequence $(O_d)_d$ is sub-Fibonacci, and that if the sequence $(O_d / O_{d-1})_d$ converges, its limit is bounded above by the golden ratio. This analysis also produces an elementary method for computing $O_d$. In addition, we derive an iterative formula for $O_d$ by exploiting a decomposition of lex-segment ideals introduced by S. Linusson in a previous work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting finite $O$-sequences of a given multiplicity Cioffi, Francesca Guida, Margherita Commutative Algebra We study the number $O_d$ of finite $O$-sequences of a given multiplicity $d$, with particular attention to the computation of $O_d$. We show that the sequence $(O_d)_d$ is sub-Fibonacci, and that if the sequence $(O_d / O_{d-1})_d$ converges, its limit is bounded above by the golden ratio. This analysis also produces an elementary method for computing $O_d$. In addition, we derive an iterative formula for $O_d$ by exploiting a decomposition of lex-segment ideals introduced by S. Linusson in a previous work. |
| title | Counting finite $O$-sequences of a given multiplicity |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2507.23438 |