A study of $v$-number for some monomial ideals
| Autor: | Biswas, Prativa, Mandal, Mousumi |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we give formulas for $v$-number of edge ideals of some graphs like path, cycle, 1-clique sum of a path and a cycle, 1-clique sum of two cycles and join of two graphs. For an $\mathfrak{m}$-primary monomial ideal $I\subset S=K[x_1,\ldots,x_t]$, we provide an explicit expression of $v$-number of $I$, denoted by $v(I)$, and give an upper bound of $v(I)$ in terms of the degree of its generators. We show that for a monomial ideal $I$, $v(I^{n+1})$ is bounded above by a linear polynomial for large $n$ and for certain classes of monomial ideals, the upper bound is achieved for all $n\geq 1$. For $\mathfrak m$-primary monomial ideal $I$ we prove that $v(I)\leq$ reg$(S/I)$ and their difference can be arbitrarily large. Comment: 15 pages |
| Databáze: | arXiv |
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