4-dissections and 8-dissections for some infinite products

Regular dissections of an infinite strip

In the early 1970s, Bro. U. Alfred Brousseau asked for the number of regions formed in an infinite strip by the mn segments that join m equally spaced points on one edge to n equally spaced points on the other. Using projective duality, we express the number of points, segments, and regions formed by Brousseau's configuration in terms of the numbers Lk(m, n) of lines that meet an m x n lattice ...

Dissections Illustrated

Parotidectomies and Neck Dissections

The organization of the following study reflects, in general, the steps of a review article in parotidectomies and neck dissections. Part one contains the nature of the parotidectomies case study report. Part two contains the Neck dissection techniques analysis which are 1. Radical (RND) 2. Modified Radical (MRND) 3. Supraomohyoid, Parotid gland surgery complications and Neck dissection complic...

Dissections, cuts and triangulations

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Polygon dissections and some generalizations of cluster complexes

Let W be a Weyl group corresponding to the root system An−1 or Bn. We define a simplicial complex ∆mW in terms of polygon dissections for such a group and any positive integer m. For m = 1, ∆ W is isomorphic to the cluster complex corresponding to W , defined in [9]. We enumerate the faces of ∆ W and show that the entries of its h-vector are given by the generalized Narayana numbers N W (i), de...