Bounds on extremal functions of forbidden patterns
Name
921857439-MIT.pdf
Description
Full printable version
Size
4.31 MB
Format
Adobe PDF
Checksum (MD5)
28f3377604ba43fe02631482b181007e
Author(s)
Geneson, Jesse (Jesse T.)
Advisor(s)
Peter Shor.
Date Issued
2015
Publisher
Massachusetts Institute of Technology
Abstract
Extremal functions of forbidden sequences and 0 - 1 matrices have applications to many problems in discrete geometry and enumerative combinatorics. We present a new computational method for deriving upper bounds on extremal functions of forbidden sequences. Then we use this method to prove tight bounds on the extremal functions of sequences of the form (12 ... 1)t for 1 >/= 2 and t >/= 1, abc(acb)t for t >/= 0, and avav'a, such that a is a letter, v is a nonempty sequence excluding a with no repeated letters and v' is obtained from v by only moving the first letter of v to another place in v. We also prove the existence of infinitely many forbidden 0 - 1 matrices P with non-linear extremal functions for which every strict submatrix of P has a linear extremal function. Then we show that for every d-dimensional permutation matrix P with k ones, the maximum number of ones in a d-dimensional matrix of sidelength n that avoids P is 20(k) nd-1
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 63-66).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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