Browsing Theses by Subject "generating series"

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Character Polynomials and Lagrange Inversion

Rattan, Amarpreet (University of Waterloo, 2005)

In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which ...
Computing the Residue Class of Partition Numbers

Shuldiner, Pavel (University of Waterloo, 2016-09-14)

In 1919, Ramanujan initiated the study of congruence properties of the integer partition function $p(n)$ by showing that $$p(5n+4) \equiv 0 \mod{5}$$ and $$p(7n+5) \equiv 0 \mod{7}$$ hold for all integers $n$. These results ...
Genus one partitions

Yip, Martha (University of Waterloo, 2006)

We obtain a tight upper bound for the genus of a partition, and calculate the number of partitions of maximal genus. The generating series for genus zero and genus one rooted hypermonopoles is obtained in closed form ...