The Boustrophedon Transform for Descent Polytopes

  • Richard EhrenborgEmail author
  • Alex Happ


We give a short proof that the f-vector of the descent polytope \({{\,\mathrm{DP}\,}}_{\mathbf {v}}\) is componentwise maximized when the word \(\mathbf {v}\) is alternating. Our proof uses an f-vector analog of the boustrophedon transform.


The boustrophedon transform Descent polytopes Alternating words f-vector 

Mathematics Subject Classification

52B05 (05A15) 



The authors are grateful to the two referees for their comments on an earlier version of this paper, including contributing the question in the concluding remark. This work was supported by a grant from the Simons Foundation (#429370, Richard Ehrenborg).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA
  2. 2.Department of MathematicsChristian Brothers UniversityMemphisUSA

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