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Browsing Theses - Mathematics by Title
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(Massachusetts Institute of Technology, 2007)In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and ...
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(Massachusetts Institute of Technology, 1965)
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(Massachusetts Institute of Technology, 1971)
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(Massachusetts Institute of Technology, 2005)In this thesis, we present bijections proving partitions identities. In the first part, we generalize Dyson's definition of rank to partitions with successive Durfee squares. We then present two symmetries for this new ...
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(Massachusetts Institute of Technology, 1994)
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(Massachusetts Institute of Technology, 2012)We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of ...
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(Massachusetts Institute of Technology, 2009)A grid shape is a set of boxes chosen from a square grid; any Young diagram is an example. We consider a notion of pattern-avoidance for 0-1 fillings of grid shapes, which generalizes permutation pattern-avoidance. A filling ...
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(Massachusetts Institute of Technology, 1992)
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(Massachusetts Institute of Technology, 1990)
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(Massachusetts Institute of Technology, 1985)
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(Massachusetts Institute of Technology, 1946)
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(Massachusetts Institute of Technology, 1994)
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(Massachusetts Institute of Technology, 2008)We study new statistics on permutations that are variations on the descent and the inversion statistics. In particular, we consider the alternating descent set of a permutation [sigma] = [sigma] 1 [sigma] 2 an defined as ...
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(Massachusetts Institute of Technology, 1973)
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(Massachusetts Institute of Technology, 1994)
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The presentation functor and Weierstrass theory for families of local complete intersection curves (Massachusetts Institute of Technology, 1994)
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(Massachusetts Institute of Technology, 1972)
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(Massachusetts Institute of Technology, 1996)
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(Massachusetts Institute of Technology, 1988)
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(Massachusetts Institute of Technology, 2005)(cont.) Packing/Covering problems, we prove upper and lower bounds on the adaptivity gap depending on the dimension. We also design polynomial-time algorithms achieving near-optimal approximation guarantees with respect ...
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