Computing linear extensions for polynomial posets subject to algebraic constraints

Shane Kepley, Konstantin Mischaikow, Lun Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small "admissible"" subset of these linear extensions, determined implicitly by the evaluation map, are of interest. This seemingly novel problem arises in the study of global dynamics of gene regulatory networks in which case the poset is a Boolean lattice. We provide an algorithm for solving this problem using linear programming for arbitrary partial orders of linear polynomials. This algorithm exploits this additional algebraic structure inherited from the polynomials to efficiently compute the admissible linear extensions. The biologically relevant problem involves multilinear polynomials, and we provide a construction for embedding it into an instance of the linear problem.

Original languageEnglish (US)
Pages (from-to)388-416
Number of pages29
JournalSIAM Journal on Applied Algebra and Geometry
Issue number2
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology
  • Applied Mathematics


  • Algebraic geometry
  • Dynamical systems
  • Linear programming
  • Order theory


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