2026-09-18T23:42:05Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1269372026-06-16T18:52:19Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Henry Cohn.
Wellens, Jake(Jake Lee)
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2020-09-03T16:42:08Z
2020-09-03T16:42:08Z
2020
2020
https://hdl.handle.net/1721.1/126937
1191267818
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 107-112).
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.
by Jake Wellens.
Ph.D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
112 pages
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Assorted results in boolean function complexity, uniform sampling and clique partitions of graphs
Thesis
application/pdf
2020-09-03T16:42:08Z
Publication
Doctoral
Math
unknown
unknown
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