Several combinatorial inequalities related to squarefree monomial ideals
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914680718491648 |
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| author | Balanescu, Silviu Cimpoeas, Mircea |
| author_facet | Balanescu, Silviu Cimpoeas, Mircea |
| contents | Let $K$ be a field and $S=K[x_1,\ldots,x_n]$, the ring of polynomials in $n$ variables, over $K$. Using the fact that the Hilbert depth is an upper bound for the Stanley depth of a quotient of squarefree monomial ideals $0\subset I\subsetneq J\subset S$, we prove several combinatorial inequalities which involve the coefficients of the polynomial $f(t)=(1+t+\cdots+t^{m-1})^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03018 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Several combinatorial inequalities related to squarefree monomial ideals Balanescu, Silviu Cimpoeas, Mircea Commutative Algebra Combinatorics 05A18, 06A07, 13C15, 13P10, 13F20 Let $K$ be a field and $S=K[x_1,\ldots,x_n]$, the ring of polynomials in $n$ variables, over $K$. Using the fact that the Hilbert depth is an upper bound for the Stanley depth of a quotient of squarefree monomial ideals $0\subset I\subsetneq J\subset S$, we prove several combinatorial inequalities which involve the coefficients of the polynomial $f(t)=(1+t+\cdots+t^{m-1})^n$. |
| title | Several combinatorial inequalities related to squarefree monomial ideals |
| topic | Commutative Algebra Combinatorics 05A18, 06A07, 13C15, 13P10, 13F20 |
| url | https://arxiv.org/abs/2307.03018 |