2014/04/08 by Yi-Huang Shen, Shen, Yi-Huang
Computer Science · Mathematics · #05E40 #05E45 #13C13 #13C14 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1404.2165
openalex publication_date 2014/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When a monomial ideal has linear quotients with respect to an admissible order of increasing support-degree, we provide two proofs of different flavors to show that it is componentwise support-linear. We also introduce the variable decomposable monomial ideals. In squarefree case, these ideals correspond to the vertex decomposable simplicial complexes. We study the relationships of the variable decomposable ideals with weakly polymatroidal ideals, weakly stable ideals and ideals with linear quotients. We also investigate the componentwise properties of all these ideals.