The P-partition generating function of a (naturally labeled) poset P is a quasisymmetric function enumerating order-preserving maps from P to Z^+. Using the Hopf algebra of posets, we give necessary conditions for two posets to have the same generating function. In particular, we show that they must have the same number of antichains of each…

In this talk, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, I will provide a framework from which we can provide conditions, which are straightforward to check, for the solvability of a large number of nonlinear scalar boundary value problems. I will begin by giving the general strategy which involves a reformulation of our…

Affine Lie algebras are infinite dimensional analogs of finite dimensional simple Lie algebras. It is known there are finitely many maximal dominant weights for any integrable highest weight representation of an affine Lie algebra. However, determining these maximal dominant weights is a nontrivial task. So far only the descriptions of these weights are known for…