Szego Seminar: "Positivity among P-Partition Enumerators."

Speaker: Nathan Lesnevitch, Washington University in Saint Louis

Abstract: Every partially ordered set (poset) P has its own unique P-partition enumerator, a generalization of partitions with the standard definition. Certain posets can be given a labeling ω, which define "strict" and "weak" relations between elements of the posets. These enumerators are quasisymmetric functions, and in the case of labeled posets are always positive with respect to the Fundamental (F-)basis. In this talk we seek to show when the difference between the enumerators of two different posets can also be positive with respect to the F-basis. We will define the notion of a jump sequence and provide necessary conditions associated with it, and we will show that a broad operation for combining posets preserves certain positivity properties. (Co-work with Peter R.W. McNamara)

Host: Nathan Wagner