Bloom syndrome (BS) is an autosomal recessive disorder characterized by a high incidence of cancer and genomic instability. BLM, the protein defective in BS, is a RecQ-like helicase, presumed to function in DNA replication, recombination, or repair. BLM localizes to promyelocytic leukemia protein (PML) nuclear bodies and is expressed during late S and G2.… (More)
We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form (1 i). Our result generalizes earlier work of Pak in which substantial restrictions were placed on the permutation being factored.
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending work of Biane. We deduce from our result a formula of Poulalhon and Schaeffer that was previously derived through an intricate combinatorial argument. Our notation… (More)
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number H α of ways a given permutation (with cycles described by the partition α) can be decomposed into a product of exactly i 2 2-cycles, i 3 3-cycles, etc., with certain minimality and transitivity conditions imposed on the… (More)
We count the number of lattice paths lying under a cyclically shifting piece-wise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical reflection argument. A refinement allows for the counting of paths with a specified number of corners. We also apply the… (More)
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Abstract The central topic of this thesis is parking functions. A parking function is a sequence of positive… (More)
In the world according to Garp, we are all terminal cases.