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Scrambled Vandermonde Convolutions of Gaussian Polynomials
- Publication Year :
- 2020
-
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.<br />Comment: 2 figures
- Subjects :
- Mathematics - Combinatorics
05A05, 05A19, 05A30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2004.01968
- Document Type :
- Working Paper