Algebraic criteria for geometric realizability

1989 ◽  
pp. 61-86
Author(s):  
Jürgen Bokowski ◽  
Bernd Sturmfels
Keyword(s):  
Geometric Realizability

scholarly journals A Face of a Projective Triangulation Removed for Its Geometric Realizability

2011 ◽  
Vol 47 (1) ◽  
pp. 215-234
Author(s):  
Atsuhiro Nakamoto ◽  
Shoichi Tsuchiya
Keyword(s):  
Geometric Realizability

scholarly journals The ν-Tamari Lattice via ν-Trees, ν-Bracket Vectors, and Subword Complexes

10.37236/8000 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Cesar Ceballos ◽  
Arnau Padrol ◽  
Camilo Sarmiento
Keyword(s):  
Point Of View ◽  
Simple Description ◽  
Adjacency Graph ◽  
Lattice Property ◽  
Combinatorial Objects ◽  
Tamari Lattice ◽  
North East ◽  
Geometric Realizability ◽  
New Interpretation ◽  
Subword Complex

We give a new interpretation of the $\nu$-Tamari lattice of Préville-Ratelle and Viennot in terms of a rotation lattice of $\nu$-trees. This uncovers the relation with known combinatorial objects such as north-east fillings, \mbox{tree-like} tableaux and subword complexes. We provide a simple description of the lattice property using certain bracket vectors of $\nu$-trees, and show that the Hasse diagram of the $\nu$-Tamari lattice can be obtained as the facet adjacency graph of certain subword complex. Finally, this point of view generalizes to multi $\nu$-Tamari complexes, and gives (conjectural) insight on their geometric realizability via polytopal subdivisions of multiassociahedra.

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