On the Hilbert depth of the quotient ring of the edge ideal of a star graph
Abstract
Abstract Let S n = K [ x 1 , . . . , x n , y ] and I n = ( x 1 y, x 2 y, . . . , x n y ) ⊂ S n be the edge ideal of star graph. We prove that hdepth ( S n / I n ) ≥ ⌈ n 2 ⌉ + ⌊ n ⌋ - 2 \left( {S_n /I_n } \right) \ge \left\lceil {{n \over 2}} \right\rceil + \left\lfloor {\sqrt n } \right\rfloor - 2 . Also, we show that for any ε > 0, there exists some integer A = A ( ε ) ≥ 0 such that hdepth ( S n / I n ) ≤ ⌈ n 2 ⌉ + ⌊ ε n ⌋ + A − 2 (S_n/I_n) \leq \lceil \frac{n}{2} \rceil + \lfloor \varepsilon n \rfloor + A - 2 . We deduce that lim n → ∞ 1 n hdepth ( S n / I n ) = 1 2 \lim_{n \to \infty} \frac{1}{n} hdepth(S_n/I_n) = \frac{1}{2} .
Fields of Study & Subjects
Commutative Algebra and Its Applications
Rings
Modules
and Algebras
Graph theory and applications
Publication details
- Journal / source
- Analele Universităţii "Ovidius" Constanţa. Seria Matematică
- Publisher
- Walter de Gruyter GmbH
- Volume
- 34
- Issue
- 2
- Pages
- 17–28
- Publication date
- 1 July 2026
- Language
- EN