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math.AC2025
The vertex covers, Betti numbers and projective dimensions of perfect binary trees
Nguyen Thu Hang, Tran Duc Dung, Do Van Kien
Let be a perfect binary tree and be its edge ideal in the polynomial ring . We determine the vertex cover number, independent number, and establish the recursive formula…
math.AC2025
Koszul property and finite linearity defect over -stretched local rings
Do Van Kien, Hop D. Nguyen
The linearity defect is a measure for the non-linearity of minimal free resolutions of modules over noetherian local rings. A tantalizing open question due to Herzog and Iyengar as…
math.AC2025
Pseudo-Frobenius numbers and defining ideals in stretched numerical semigroup rings
Do Van Kien, Naoyuki Matsuoka, Taiga Ozaki
The pseudo-Frobenius numbers of a numerical semigroup are deeply connected to the structure of the defining ideal of its semigroup ring . In this paper, we resolve a cert…