Won Chul Yang

A Macaulay-Type Lower Bound for Nested Multichains and Lecture Hall Polytopes

Macaulay's theorem bounds the growth of the Hilbert function of a standard graded algebra from above: H(d+1) ≤ H(d)^ . We prove lower bounds of the same type for a natural combinatorial family. Let A_1 ⊆ A_2 ⊆ ... be finite subsets of a totally ordered set and let h(D) count the...