2020/04/04 by Magnus Aspenberg, Aspenberg, Magnus, Rodrigo A. Pérez +1
Computer Science · Mathematics · #05A05 #05A19 #05A30 #Advanced Combinatorial Mathematics #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2004.01968
openalex publication_date 2020/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.