Combinatorial reciprocity theorems

Combinatorial Reciprocity Theorems Enumerative Combinatorics with a Polyhedral Angle

Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics

simplicial complex, 122, 136,164acyclic orientation, 5, 218affine hull, 52affine projection, 56alcoved polytope, 227alcoved triangulation, 228alcoves, 227Andrews, George, 125anti-isomorphic, 239anti-symmetric, 11antichain, 13, 28, 182antistar, 168Appel, Kenneth, 2, 20arrangement of hyperplanes, 59, 74, 215ascent, 171, 191big, 235<l...

Matthias Beck & Raman Sanyal Combinatorial Reciprocity Theorems A Snapshot of Enumerative Combinatorics from a

Combinatorial reciprocity for Monotone Triangles

The number of Monotone Triangles with bottom row k1 < k2 < · · · < kn is given by a polynomial α(n; k1, . . . , kn) in n variables. The evaluation of this polynomial at weakly decreasing sequences k1 ≥ k2 ≥ · · · ≥ kn turns out to be interpretable as signed enumeration of new combinatorial objects called Decreasing Monotone Triangles. There exist surprising connections between the two classes o...

Iterated combinatorial density theorems