Combinatorial interpretations of the Kreweras triangle in terms of subset tuples

TL;DR

This paper establishes bijective combinatorial interpretations of the Kreweras triangle, connecting various models such as subset tuples, Dumont permutations, and Dellac configurations, thereby unifying different combinatorial frameworks.

Contribution

It introduces a new combinatorial interpretation of the Kreweras triangle and demonstrates its equivalence to existing models, extending the understanding of these structures.

Findings

Bijective equivalence between subset tuples and Dumont permutations

Extension of interpretations to the Kreweras triangle

Unified combinatorial framework for median Genocchi numbers

Abstract

We show how the combinatorial interpretation of the normalized median Genocchi numbers in terms of multiset tuples, defined by Hetyei in his study of the alternation acyclic tournaments, is bijectively equivalent to previous models like the normalized Dumont permutations or the Dellac configurations, and we extend the interpretation to the Kreweras triangle.