Assorted results in boolean function complexity, uniform sampling and clique partitions of graphs
Name
1191267818-MIT.pdf
Size
900.43 KB
Format
Adobe PDF
Checksum (MD5)
817c2595f662ea0b52bd792ac0a934b8
Author(s)
Wellens, Jake(Jake Lee)
Advisor(s)
Henry Cohn.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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