The edge ideals of {{\textbf{t}}}-spread d-partite hypergraphs

Musapaşaoğlu, Asli ^[1] ; Asloob Qureshi, Ayesha ^[1] ; Nasernejad, Mehrdad ^[2]
1. [1] Sabanci University, Faculty of Engineering and Natural Sciences, Orta Mahalle, Tuzla, 34956, Istanbul, Turkey
2. [2] Univ. Artois, UR 2462, Laboratoire de Mathématique de Lens (LML), 62300, Lens, France
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 735-751
Idioma: inglés
DOI: 10.1007/s13348-023-00410-y
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Resumen
- Inspired by the definition of {{\textbf{t}}}-spread monomial ideals, in this paper, we introduce {{\textbf{t}}}-spread d-partite hypergraph {\text {K}}^{{{\textbf{t}}}}_{{\text {V}}} and study its edge ideal I({\text {K}}^{{{\textbf{t}}}}_{{\text {V}}}). We prove that I({\text {K}}^{{{\textbf{t}}}}_{{\text {V}}}) has linear quotients, all powers of I({\text {K}}^{{{\textbf{t}}}}_{{\text {V}}}) have linear resolution and the Rees algebra of I({\text {K}}^{{{\textbf{t}}}}_{{\text {V}}}) is a normal Cohen-Macaulay domain. It is also shown that I (Kv) is normally torsion-free and a complete characterization of Cohen-Macaulay S/I({\text {K}}^{{{\textbf{t}}}}_{{\text {V}}}) is given.