Browsing Department of Mathematics by Title
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Combinatorics of permutation patterns, interlacing networks, and Schur functions
(Massachusetts Institute of Technology, 2015)In the first part, we study pattern avoidance and permutation statistics. For a set of patterns n and a permutation statistic st, let Fst/n ([Pi]; q) be the polynomial that counts st on the permutations avoiding all patterns ... 
The combinatorics of reduced decompositions
(Massachusetts Institute of Technology, 2006)This thesis examines several aspects of reduced decompositions in finite Coxeter groups. Effort is primarily concentrated on the symmetric group, although some discussions are subsequently expanded to finite Coxeter groups ... 
Combinatorics of ribbon tableaux
(Massachusetts Institute of Technology, 2005)This thesis begins with the study of a class of symmetric functions ... Which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of ... 
Combinatorics related to the totally nonnegative Grassmannian
(Massachusetts Institute of Technology, 2011)In this thesis we study the combinatorial objects that appear in the study of nonnegative part of the Grassmannian. The classical theory of total positivity studies matrices such that all minors are nonnegative. Lustzig ... 
A compact moduli space for CohenMacaulay curves in projective space
(Massachusetts Institute of Technology, 2004)We define a moduli functor parametrizing finite maps from a projective (locally) CohenMacaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most ... 
Compactified Jacobians of integral curves with double points
(Massachusetts Institute of Technology, 1997) 
Compactness results for pseudoholomorphic curves in symplectic cobordisms
(Massachusetts Institute of Technology, 2000) 
Comparing products of Schur functions and quasisymmetric functions
(Massachusetts Institute of Technology, 2007)In this thesis a conjecture of Okounkov, a conjecture of FominFultonLiPoon, and a special case of LascouxLeclercThibon's conjecture on Schur positivity of certain differences of products of Schur functions are proved. ... 
Complete integrability and geometrically induced representations
(Massachusetts Institute of Technology, 1991) 
A complexity theoretic approach to learning
(Massachusetts Institute of Technology, 2002)This thesis details a new vantage point for attacking longstanding problems in machine learning. We use tools from computational complexity theory to make progress on problems from computational learning theory. Our methods ... 
Compressed absorbing boundary conditions for the Helmholtz equation
(Massachusetts Institute of Technology, 2014)Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible ... 
The Compression Theorem of Rourke and Sanderson
(Massachusetts Institute of Technology, 2006)This is an exposition of the Compression Theorem of Colin Rourke and Brian Sanderson, which leads to a new proof of the Immersion Theorem. 
Compressive algorithms for search and storage in biological data
(Massachusetts Institute of Technology, 2017)Disparate biological datasets often exhibit similar welldefined structure; efficient algorithms can be designed to exploit this structure. In this doctoral thesis, we present a framework for similarity search based on ... 
A computation of the action of the mapping class group on isotopy classes of curves and arcs in surfaces
(Massachusetts Institute of Technology, 1982) 
Computational applications of noise sensitivity
(Massachusetts Institute of Technology, 2003)This thesis is concerned with the study of the noise sensitivity of boolean functions and its applications in theoretical computer science. Noise sensitivity is defined as follows: Let f be a boolean function and let ... ... 
Computational methods for higher real Ktheory with applications to tmf
(Massachusetts Institute of Technology, 2006)We begin by present a new Hopf algebra which can be used to compute the tmf homology of a space or spectrum at the prime 3. Generalizing work of Mahowald and Davis, we use this Hopf algebra to compute the tmf homology of ... 
A computational model of skill acquisition.
(Massachusetts Institute of Technology, 1973) 
Computational neutronics analysis of TRIGA reactors during power pulsing
(Massachusetts Institute of Technology, 2011)Training, Research, Isotopes, General Atomics (TRIGA) reactors have the unique capability of generating high neutron flux environments with the removal of a transient control rod, creating conditions observed in fast fission ... 
Computationally efficient errorcorrecting codes and holographic proofs
(Massachusetts Institute of Technology, 1995) 
A computeraided combinatorial analysis of the game of cribbage
(Massachusetts Institute of Technology, 1992)