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math.CO2023
Ubiquity of power sums in graph profiles
Grigoriy Blekherman, Annie Raymond
Graph density profiles are fundamental objects in extremal combinatorics. Very few profiles are fully known, and all are two-dimensional. We show that even in high dimensions ratio…
math.CO2023
Tropicalizing the Graph Profile of Some Almost-Stars
Maria Dascălu, Annie Raymond
Many important problems in extremal combinatorics can be stated as certifying polynomial inequalities in graph homomorphism numbers, and in particular, many ask to certify pure bin…
math.CO2023
Generalized Pitman-Stanley polytope: vertices and faces
William T. Dugan, Maura Hegarty, Alejandro H. Morales +1
In 1999, Pitman and Stanley introduced the polytope bearing their name along with a study of its faces, lattice points, and volume. The Pitman-Stanley polytope is well-studied due…