1. Scrambled Vandermonde Convolutions of Gaussian Polynomials
- Author
-
Aspenberg, Magnus and Pérez, Rodrigo
- Subjects
Mathematics - Combinatorics ,05A05, 05A19, 05A30 - Abstract
It is well known that Gaussian polynomials (i.e., $q$-binomials) describe the distribution of the $area$ statistic on monotone paths in a rectangular grid. We introduce two new statistics, $corners$ and $cindex$; attach ``ornaments'' to the grid; and re-evaluate these statistics, in order to argue that all scrambled versions of the $cindex$ statistic are equidistributed with $area$. Our main result is a representation of the generating function for the bi-statistic $(cindex,corners)$ as a two-variable Vandermonde convolution of the original Gaussian polynomial. The proof relies on explicit bijections between differently ornated paths., Comment: 2 figures
- Published
- 2020