## Abstract

It is well known that Gaussian polynomials (i.e., q-binomials) describe the distribution of the [Formula presented] statistic on monotone paths in a rectangular grid. We introduce two new statistics, [Formula presented] and [Formula presented]; attach “ornaments” to the grid that scramble the values of [Formula presented] in specific fashion; and re-evaluate these statistics, in order to argue that all scrambled versions of the [Formula presented] statistic are equidistributed with [Formula presented]. Our main result is a representation of the generating function for the bi-statistic [Formula presented] as a new, two-variable Vandermonde convolution of the original Gaussian polynomial. The proof relies on explicit bijections between differently ornated paths.

Original language | English |
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Article number | 113064 |

Journal | Discrete Mathematics |

Volume | 345 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2022 |

## Subject classification (UKÄ)

- Mathematics

## Free keywords

- Gaussian polynomials
- Integer partitions
- Lattice paths
- q-binomials
- q-Vandermonde convolution