Positivity aspects of complete homogeneous symmetric polynomials (Stephan Garcia, Pomona)

Hunter’s theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions.  We provide new proofs of Hunter’s theorem, applications to operator theory, and a noncommutative (NC) generalization that sheds light even on the commutative case.  Surprisingly, this work emerged from a problem in analytic combinatorics.