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Hurwitz numbers with completed cycles and Gromov--Witten theory relative to at most three points
Ricky X. F. Chen, Zhen-Ran Wang
Hurwitz numbers with completed cycles are standard Hurwitz numbers with simple branch points replaced by completed cycles. In fact, simple branch points correspond to completed …
Towards studying the structure of triple Hurwitz numbers
Ricky Xiao-Feng Chen
Going beyond the studies of single and double Hurwitz numbers, we report some progress towards studying Hurwitz numbers which correspond to ramified coverings of the Riemann sphere…
The Harer-Zagier and Jackson formulas and new results for one-face bipartite maps
Ricky X. F. Chen
The study of bipartite maps (or Grothendieck's dessins d'enfants) is closely connected with geometry, mathematical physics and free probability. Here we study these objects from th…
The minimum number of chains in a noncrossing partition of a poset
Ricky X. F. Chen
The notion of noncrossing partitions of a partially ordered set (poset) is introduced here. When the poset in question is with the complete order of natural…