2022/03/03 by Kamalesh Saha, Saha, Kamalesh, Indranath Sengupta +1
Computer Science · Mathematics · #05C22 #05C25 #13F20 #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2203.01710
openalex publication_date 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of the edge ideal I(DG) of a weighted oriented graph DG with underlying graph G started in the context of Reed-Muller type codes. We generalize a Cohen-Macaulay construction for I(DG), which Villarreal gave for edge ideals of simple graphs. We use this construction to classify all the Cohen-Macaulay weighted oriented edge ideals, whose underlying graph is a cycle. We show that the conjecture on Cohen-Macaulayness of I(DG), proposed by Pitones et al. (2019), holds for I(D_Cn), where Cn denotes the cycle of length n. Miller generalized the concept of Alexander dual ideals of square-free monomial ideals to arbitrary monomial ideals, and in that direction, we study the Alexander dual of I(DG) and its conditions to be Cohen-Macaulay.