• Corpus ID: 211020896

Enumerative problems for arborescences and monotone paths on polytopes

  title={Enumerative problems for arborescences and monotone paths on polytopes},
  author={Christos A. Athanasiadis and Jes{\'u}s A. De Loera and Zhenyang Zhang},
  journal={arXiv: Combinatorics},
Every generic linear functional $f$ on a convex polytope $P$ orients the edges of the graph of $P$. In this directed graph one can define a notion of $f$-arborescence and $f$-monotone path on $P$. Additionally, a natural notion of adjacency between pairs of $f$-monotone paths gives us the so called flip graph of $f$-monotone paths. These concepts are of importance in geometric combinatorics and optimization. We investigate the extreme values of the number of $f$-arborescences, the number of $f… 
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