Now showing items 1-3 of 3

• Combinatorial Methods for Enumerating Maps in Surfaces of Arbitrary Genus ﻿

(University of Waterloo, 2016-06-10)
The problem of map enumeration is one that has been studied intensely for the past half century. Early work on this subject included the works of Tutte for various types of rooted planar maps and the works of Brown for ...
• Computing the Residue Class of Partition Numbers ﻿

(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 ...
• Induction Relations in the Symmetric Groups and Jucys-Murphy Elements ﻿

(University of Waterloo, 2018-08-16)
Transitive factorizations faithfully encode many interesting objects. The well-known ones include ramified coverings of the sphere and hypermaps. Enumeration of specific classes of such objects have been known for quite ...

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