Further extensions of Haglund-Remmel-Wilson identity

Abstract

MacMahon's equidistribution theorem states that the permutation statistics inversion number and major index are equidistributed. In 2015, Remmel and Wilson proved a conjectured identity of Haglund which is an extension of MacMahon's equidistribution theorem to ordered set partitions. Recently, Liu extended this identity to k-Stirling permutations and posed a conjecture concerning an ascent analogue of his extension. In this paper, we shall present a combinatorial proof of this conjecture. Furthermore, we derive an analogous result for another maj-like statistic introduced by Liu.