Date of Award
2017
Document Type
Open Access Master's Thesis
Degree Name
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
William Keith
Committee Member 1
Fabrizio Zanello
Committee Member 2
Durdu Guney
Abstract
We begin with a discussion of the symmetricity of $\maj$ over $\des$ in pattern avoidance classes, and its relationship to $\maj$-Wilf equivalence. From this, we explore the distribution of permutation statistics across pattern avoidance for patterns of length 3 and 4.
We then begin discussion of Han's bijection, a bijection on permutations which sends the major index to Denert's statistic and the descent number to the (strong) excedance number. We show the existence of several infinite families of fixed points for Han's bijection.
Finally, we discuss the image of pattern avoidance classes under Han's bijection, for the purpose of finding a condition which has the same distribution of $\den$ over $\exc$ as pattern avoidance does of $\maj$ over $\des$.
Recommended Citation
Davies, Joshua Thomas Agustin, "Distribution of permutation statistics across pattern avoidance classes, and the search for a Denert-associated condition equivalent to pattern avoidance", Open Access Master's Thesis, Michigan Technological University, 2017.