Counting polygon dissections in the projective plane (Q953906)

The number of ways to dissect a polygon in the projective plane into \(n\) subpolygons with \(k+1\) sides each is determined using generating functions. In particular, for \(k=2\) the number of triangulations of a polygon in the projective plane is determined which was first done by \textit{P.H. Edelman} and \textit{V Reiner} in [``Catalan triangulations of the Möbius band'', Graphs Comb. 13, No.\,3, 231--243 (1997; Zbl 0890.05034)]. Moreover, asymptotic estimates for the number of dissections of various kinds are obtained and probability limit laws for natural parameters associated to triangulations and dissections are determined.