Janet's Algorithm

TL;DR

This paper introduces Janet's algorithm for Stanley decomposition of monomial ideals, demonstrating its effectiveness for squarefree ideals and its application in partitioning simplicial complexes.

Contribution

The paper presents Janet's algorithm as a new method for Stanley decomposition and shows its utility for squarefree monomial ideals and simplicial complex partitions.

Findings

Janet's algorithm computes Stanley decompositions for monomial ideals.

The algorithm produces squarefree Stanley decompositions for squarefree ideals.

It also provides a partitioning method for simplicial complexes.

Abstract

We have introduced the Janet's algorithm for the Stanley decomposition of a monomial ideal I in a polynomial ring S = K[x_1,...,x_n] and prove that Janet's algorithm gives the squarefree Stanley decomposition of S/I for a squarefree monomial ideal I. We have also shown that the Janet's algorithm gives a partition of a simplicial complex.