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Polymatroidal property of generalized mixed product ideals

Monica La Barbiera, Roya Moghimipor

Abstract

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper, we study the polymatroidal property of generalized mixed product ideals. Furthermore, some algebraic invariants of L are computed.

Polymatroidal property of generalized mixed product ideals

Abstract

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper, we study the polymatroidal property of generalized mixed product ideals. Furthermore, some algebraic invariants of L are computed.
Paper Structure (3 sections, 15 theorems, 29 equations)

This paper contains 3 sections, 15 theorems, 29 equations.

Table of Contents

  1. Introduction
  2. Polymatroidal ideals
  3. Linear quotients of generalized mixed product ideals

Key Result

Theorem 2.2

Let $L=I_{q}J_{r}\subset K[x_1,\ldots, x_n,y_1, \ldots, y_m]$ be the generalized mixed product ideal, where for integers $a$ and $b$, the ideal $I_a$ (resp. $J_b$) is the ideal generated by all squarefree monomials of degree $a$ in the polynomial ring $K[x_1,\ldots, x_n]$ (resp. of degree $b$ in the

Theorems & Definitions (34)

  • Example 2.1
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • proof
  • Theorem 2.4
  • proof
  • Example 2.5
  • Proposition 2.6
  • proof
  • ...and 24 more