Inspired by the k-inversion statistic for LLT polynomials, we define a k-inversion number and k-descent set for words. Using these, we define a new statistic on words, called the k-major index, that interpolates between the major index and inversion number. We give a bijective proof that the k-major index is equi-distributed with the major index, generalizing a classical result of Foata and rediscovering a result of Kadell. Inspired by recent work of Haglund and Stevens, we give a partial… CONTINUE READING

A new class of symmetric functions, Actes du 20e Séminaire Lotharingien de Combinatoire

I. G. Macdonald

Publ. I.R.M.A. Strasbourg, • 1988

The Indices of Permutations and the Derivation Therefrom of Functions of a Single Variable Associated with the Permutations of any Assemblage of Objects