Consequences of the packing problem

no code implementations • 11 Jan 2021 • Hrishikesh Bodas, Benjamin Drabkin, Caleb Fong, Su Jin, Justin Kim, Wenxuan Li, Alexandra Seceleanu, Tingting Tang, Brendan Williams

We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals.

Combinatorial Optimization Commutative Algebra Combinatorics 13C70, 13F55, 05E40, 05C65, 05C15

Convex bodies and asymptotic invariants for powers of monomial ideals

no code implementations • 11 Jan 2021 • João Camarneiro, Benjamin Drabkin, Duarte Fragoso, William Frendreiss, Daniel Hoffman, Alexandra Seceleanu, Tingting Tang, Sewon Yang

Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals.

Commutative Algebra Combinatorics 13F55, 13F20, 52B20, 14M25