Thanh Vu

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20232026

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Showing 2024 · math.ACShow all

4 papers · 2 filters

math.AC2024

Multiplicity of powers of squarefree monomial ideals

Phan Thi Thuy, Thanh Vu

Let $I$ be an arbitrary nonzero squarefree monomial ideal of dimension $d$ in a polynomial ring $S = k [x_{1}, \dots, x_{n}]$ . Let $μ$ be the number of associated primes of $S/I…

math.AC2024

Graded Betti numbers of powers of path ideals of paths

Silviu Balanescu, Mircea Cimpoeas, Thanh Vu

Let $I_{n, m} = (x_{1} \dots x_{m}, x_{2} \dots x_{m + 1}, \dots, x_{n + 1} x_{n + 2} \dots x_{n + m})$ be the $m$ -path ideal of a path of length $n + m - 1$ over a polynomial ring $S = \mathrm{k}[…

math.AC2024

Betti numbers of powers of path ideals of cycles

Silviu Balanescu, Mircea Cimpoeas, Thanh Vu

Let $J_{n, m} = (x_{1} \dots x_{m}, x_{2} \dots x_{m + 1}, \dots, x_{n} x_{1} \dots x_{m - 1})$ be the $m$ -path ideal of a cycle of length $n \geq 5$ over a polynomial ring $S = k[x_1,\ldots,x_n…

math.AC2024

Projective dimension and regularity of 3-path ideals of unicyclic graphs

Nguyen Thu Hang, Thanh Vu

We compute the projective dimension and regularity of $3$ -path ideals of arbitrary graphs with at most one cycle.