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, 235number, 2022-ascent, 235 Barlow, Peter, 125Barvinok, Alexander, 173barycenter, 229base orientation, 248Batyrev, Victor, 173Bell, Eric Temple, 43beneath, 77Bernoulli number, 127Bernoulli polynomial, 127, 208Betke, Ulrich, 173beyond, 77, 148big ascent, 235binomial coefficient, xii, 90, 97binomial theorem, 30, 43, 90Birkhoff lattice, 28, 193Birkhoff’s theorem, 35Birkhoff, Garrett, 43Birkhoff, George, 2, 20Boolean arrangement, 85characteristic polynomial of, 223Boolean lattice, 32, 38, 124boundary, 52boundary complex, 163braid arrangement, 85characteristic polynomial of, 223Breuer, Felix, 21Brianchon, Charles Julien, 80Brianchon–Gram relation, 76, 86, 155bridge, 7, 251Brion’s theorem, 156Brion, Michel, 173Bruggesser, Heinz, 79 calculus, 91canonical realization, 165Cayley, Arthur, 125cell, 136central, 75centrally-symmetric polytope, 232chain, 12, 182maximal, 36saturated, 34chain partitioncombinatorial reciprocity theorem for,121(Π, φ)-chain partition, 119, 167