# A note on the distribution of major index for Schr\"oder paths

**Authors:** Xiaomei Chen

arXiv: 1906.09018 · 2019-06-24

## TL;DR

This paper corrects an error in previous formulas regarding the distribution of the major index for Schr"oder paths and provides a complete proof for all cases, enhancing the mathematical understanding of these combinatorial objects.

## Contribution

It rectifies a mistake in earlier work and extends the proof to cover all cases of the distribution of the major index for Schr"oder paths.

## Key findings

- Corrected the proof of the distribution formulas for Schr"oder paths
- Extended the proof to all cases beyond E<D<N
- Ensured the formulas are valid universally

## Abstract

Bonin, Shapiro and Simion (1993) gave two formulas on the distribution of major index for Schr\"oder paths, and proved their result for the case $E<D<N$. In this short note, we correct an error in their proof, and give a complete proof for all cases.

## Full text

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## References

3 references — full list in the complete paper: https://tomesphere.com/paper/1906.09018/full.md

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Source: https://tomesphere.com/paper/1906.09018