Lattice Paths, Lefschetz Properties, and Almkvist's Conjecture in Two Variables
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913387298947072 |
|---|---|
| author | Abdallah, Nancy McDaniel, Chris |
| author_facet | Abdallah, Nancy McDaniel, Chris |
| contents | We study a certain two-parameter family of non-standard graded complete intersections $A(m,n)$. In case $n=2$, we show that $A(m,2)$ has the strong Lefschetz property and the complex Hodge-Riemann property if and only if $m$ is even. This supports a strengthening of a conjecture of Almkvist on the unimodality of the Hilbert function of $A(m,n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattice Paths, Lefschetz Properties, and Almkvist's Conjecture in Two Variables Abdallah, Nancy McDaniel, Chris Commutative Algebra 13E10, 05A10, 05B20, 11B83, 13H10, 14F45, 15A15, 20F55 We study a certain two-parameter family of non-standard graded complete intersections $A(m,n)$. In case $n=2$, we show that $A(m,2)$ has the strong Lefschetz property and the complex Hodge-Riemann property if and only if $m$ is even. This supports a strengthening of a conjecture of Almkvist on the unimodality of the Hilbert function of $A(m,n)$. |
| title | Lattice Paths, Lefschetz Properties, and Almkvist's Conjecture in Two Variables |
| topic | Commutative Algebra 13E10, 05A10, 05B20, 11B83, 13H10, 14F45, 15A15, 20F55 |
| url | https://arxiv.org/abs/2404.05098 |