Assorted results in boolean function complexity, uniform sampling and clique partitions of graphs

This thesis consists of three disparate parts. In the first, we generalize and extend recent ideas of Chiarelli, Hatami and Saks to obtain new bounds on the number of relevant variables for a boolean function in terms of its degree, its sensitivity, and its certificate and decision tree complexities, and we also sharpen the best-known polynomial relationships between some of these complexity measures by a constant factor. In the second part, we show that the Partial Rejection Sampling method of Guo, Jerrum and Liu can solve a handful of natural sampling problems that fall outside the guarantees of the authors' original analysis. Finally, we revise and make partial progress on a conjecture of De Caen, Erdős, Pullman and Wormald on clique partitions of a graph and its complement, building on ideas of Keevash and Sudakov.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Wellens, Jake(Jake Lee)

Advisor dc:contributor.advisor

• Henry Cohn.

• Mathematics.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/126937

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/126937