2022/08/22 by Alessandra Costantini, Costantini, Alessandra, Alexandra Seceleanu +1
Computer Science · Mathematics · #05E40. Secondary: 13B22 #13F55 #14M25 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary: 13C70 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2208.10476
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly stable monomial ideals. In this paper we focus on algebraic and combinatorial properties of symmetric strongly shifted ideals. On the algebraic side, we elucidate properties that pertain to behavior under ideal operations, primary decomposition, and the structure of their Rees algebra. On the combinatorial side, we develop a notion of partition Borel generators which leads to connections to discrete polymatroids, convex polytopes, and permutohedral toric varieties.