Advanced Search
DSpace@MIT

Browsing Department of Mathematics by Title

Research and Teaching Output of the MIT Community

Browsing Department of Mathematics by Title

Sort by: Order: Results:

  • 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 ...
  • 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 ...
  • 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, ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Gagné, Mathieu (Massachusetts Institute of Technology, 1997)
  • 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 ...
  • 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. ...
  • Grossberg, Michael David (Massachusetts Institute of Technology, 1991)
  • 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 ...
  • 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 ...
  • Mellis, Daniel (Daniel Paul) (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.
  • O'Donnell, Ryan William, 1979- (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 ... ...
  • Spielman, Daniel Alan (Massachusetts Institute of Technology, 1995)
  • Hill, Michael Anthony, Ph. D. Massachusetts Institute of Technology (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 ...
MIT-Mirage