A Generalized Major Index Statistic

@inproceedings{Assaf2008AGM,
  title={A Generalized Major Index Statistic},
  author={Sami H. Assaf},
  year={2008}
}
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

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