Counting quiddities of polygon dissections

TL;DR

This paper introduces a novel and challenging problem of enumerating the unique quiddities of polygon dissections, extending beyond simple enumeration to a more complex combinatorial classification.

Contribution

It formulates a new open problem in combinatorics, focusing on counting distinct quiddities of polygon dissections, which has not been previously addressed.

Findings

Problem formulation for counting quiddities

Highlights the complexity of the enumeration task

Sets the stage for future research in polygon dissection classification

Abstract

We formulate the following general problem. To the best of our knowledge, it is open and has not previously been considered. It seems (at least to us!) to be difficult; at any rate, more difficult than enumerating the dissections themselves. Enumerate the distinct quiddities of dissections of the $N$-gon into $m$ cells.