Department of Mathematics

Combinatorics and Graph Theory

  •  Josh Hallam, Loyola Marymount University
  •  Whitney Duals of Graded Posets, Zoom https://msu.zoom.us/j/5476724571
  •  09/30/2020
  •  3:00 PM - 3:50 PM
  •  Online (virtual meeting)

To each graded poset one can associate two sequences of numbers; the Whitney numbers of the first kind and the Whitney numbers of the second kind. One sequence keeps track of the Möbius function at each rank level and the other keeps track of the number of elements at each rank level. The Whitney numbers appear in many contexts in combinatorics. For example, they appear as the coefficients of the chromatic polynomial of a graph and can be used to compute the number of regions in a real hyperplane arrangement. We say that posets P and Q are Whitney duals if the Whitney numbers of the first kind of P are the Whitney numbers of the second kind of Q and vice-versa. In this talk, we will discuss a method to construct Whitney duals using edge labelings and quotient posets. We will also discuss some applications of Whitney duals. This is joint work with Rafael S. González D'León.

 

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