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Browsing Theses - Dept. of Mathematics by Title

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Browsing Theses - Dept. of Mathematics by Title

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  • Combinatorial enumeration of weighted Catalan numbers 
    An, Junkyu (Massachusetts Institute of Technology, 2010)
    This thesis is devoted to the divisibility property of weighted Catalan and Motzkin numbers and its applications. In Chapter 1, the definitions and properties of weighted Catalan and Motzkin numbers are introduced. Chapter ...
  • A combinatorial flag space 
    Babson, Eric Kendall (Massachusetts Institute of Technology, 1994)
  • Combinatorial methods in multilinear algebra 
    Ehrenborg, Jöns Richard Gustaf (Massachusetts Institute of Technology, 1993)
  • Combinatorial properties of shifted complexes 
    Klivans, Caroline J. (Caroline Jane), 1977- (Massachusetts Institute of Technology, 2003)
    In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face ...
  • Combinatorics in Schubert varieties and Specht modules 
    Yoo, Hwanchul (Massachusetts Institute of Technology, 2011)
    This thesis consists of two parts. Both parts are devoted to finding links between geometric/algebraic objects and combinatorial objects. In the first part of the thesis, we link Schubert varieties in the full flag variety ...
  • Combinatorics of acyclic orientations of graphs : algebra, geometry and probability 
    Iriarte Giraldo, Benjamin (Massachusetts Institute of Technology, 2015)
    This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertex-set with a totally ordered set, ...
  • The combinatorics of adinkras 
    Zhang, Yan, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2013)
    Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory ...
  • Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields 
    Morales, Alejandro Henry (Massachusetts Institute of Technology, 2012)
    In the first part of this thesis we study factorizations of the permutation (1; 2,..., n) into k factors of given cycle type. Using representation theory, Jackson obtained for each k an elegant formula for counting these ...
  • Combinatorics of determinantal identities 
    Konvalinka, Matjaž (Massachusetts Institute of Technology, 2008)
    In this thesis, we apply combinatorial means for proving and generalizing classical determinantal identities. In Chapter 1, we present some historical background and discuss the algebraic framework we employ throughout the ...
  • Combinatorics of permutation patterns, interlacing networks, and Schur functions 
    Trongsiriwat, Wuttisak (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 
    Tenner, Bridget Eileen (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 
    Lam, Thomas F. (Thomas Fun Yau) (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 
    Oh, SuHo (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 ...
  • Compactified Jacobians of integral curves with double points 
    Gagné, Mathieu (Massachusetts Institute of Technology, 1997)
  • A compact moduli space for Cohen-Macaulay curves in projective space 
    Hønsen, Morten Oskar, 1973- (Massachusetts Institute of Technology, 2004)
    We define a moduli functor parametrizing finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most ...
  • Compactness results for pseudo-holomorphic curves in symplectic cobordisms 
    Young, Carmen M (Massachusetts Institute of Technology, 2000)
  • Comparing products of Schur functions and quasisymmetric functions 
    Pylyavskyy, Pavlo (Massachusetts Institute of Technology, 2007)
    In this thesis a conjecture of Okounkov, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity of certain differences of products of Schur functions are proved. ...
  • Complete integrability and geometrically induced representations 
    Grossberg, Michael David (Massachusetts Institute of Technology, 1991)
  • A complexity theoretic approach to learning 
    Klivans, Adam R (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 
    Bélanger-Rioux, Rosalie (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 ...
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