TL;DR
This paper explores the use of Bar Codes, combinatorial objects, to analyze Janet-like divisions, enabling the computation of nonmultiplicative powers and detection of set completeness in monomial ideals.
Contribution
It introduces a novel application of Bar Codes to Janet-like divisions, providing methods to compute nonmultiplicative powers and assess set completeness.
Findings
Bar Codes can be used to compute Janet-like nonmultiplicative powers
The method detects the completeness of a set of terms
Observations on computing Janet-like bases are presented
Abstract
Bar Codes are combinatorial objects encoding many properties of monomial ideals. In this paper we employ these objects to study Janet-like divisions. Given a finite set of terms U, from its Bar Code we can compute the Janet-like nonmultiplicative power of its elements and detect completeness of the set. Some observation on the computation of Janet-like bases conclude the work.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Topological and Geometric Data Analysis