Abstract:

Both the noncrossing partition/Kreweras poset and parking
functions are well-studied objects in combinatorics. In 1997 Richard
Stanley found a bijection between the maximal chains in the poset
and parking functions. We investigated what happens under the
bijection when we restrict the noncrossing partition poset to
certain induced subposets (certain bond posets). I will describe
all the posets involved, and the enumeration of maximal chains
in them, as well as discuss the image of Stanley's map. I will also
describe how we map the maximal chains to unimodal forests. This is
joint with Shreya Ahirwar, Davy Brooks, Parikshita Gya, Pamela
E. Harris, Max Hlavacek, Nguyen Pham, Sophie Rubenfeld, Bianca Teves,
Andrés R. Vindas-Meléndez, and Dan Khanh Vo.