On flow polytopes, order polytopes, and certain faces of the alternating sign matrix polytope

DOI10.1007/s00454-019-00073-2zbMath1414.05029arXiv1510.03357OpenAlexW2962699500MaRDI QIDQ2421594

Jessica Striker, Alejandro H. Morales, Karola Mészáros

Publication date: 17 June 2019

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.03357

zbMATH Keywords

triangulationsalternating sign matricesorder polytopesChan-Robbins-Yuen polytopeflow polytopes

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of representation theory (05E10) Combinatorial inequalities (05A20) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Directed graphs (digraphs), tournaments (05C20) Shellability for polytopes and polyhedra (52B22) Flows in graphs (05C21)

Related Items

Refinements and symmetries of the Morris identity for volumes of flow polytopes, Triangulations, Order Polytopes, and Generalized Snake Posets, The volume of the caracol polytope, On framed triangulations of flow polytopes, the \(\nu\)-Tamari lattice and Young's lattice, Column-convex matrices, \(G\)-cyclic orders, and flow polytopes, Volumes of flow polytopes related to caracol graphs, Kostant's partition function and magic multiplex juggling sequences, Gelfand--Tsetlin Polytopes: A Story of Flow and Order Polytopes, A combinatorial model for computing volumes of flow polytopes, Volumes and Ehrhart polynomials of flow polytopes

Uses Software

• SageMath
• OEIS

Cites Work

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• Enumeration formulas for Young tableaux in a diagonal strip
• A generating function for all semi-magic squares and the volume of the Birkhoff polytope
• Higher SPIN alternating sign matrices
• Kostant partitions functions and flow polytopes
• The alternating sign matrix polytope
• Alternating sign matrices and descending plane partitions
• Two poset polytopes
• Extreme points and adjacency relationship in the flow polytope
• Reduced words and plane partitions
• The Ehrhart polynomial of the Birkhoff polytope
• Proof of a conjecture of Chan, Robbins, and Yuen
• From generalized permutahedra to Grothendieck polynomials via flow polytopes
• New symmetric plane partition identities from invariant theory work of De Concini and Procesi
• Computing the Continuous Discretely
• The asymptotic volume of the Birkhoff polytope
• On the Volume of a Certain Polytope
• Quadrant marked mesh patterns in 132-avoiding permutations I
• Flow Polytopes of Signed Graphs and the Kostant Partition Function