Kyungyong Lee
On cluster variables of rank two acyclic cluster algebras.
Thu, 08/12/2010 - 15:01 — SomNambulAuthors: Kyungyong Lee
Subjects: Combinatorics
AbstractIn this note, we find an explicit formula for the Laurent expression of
cluster variables of coefficient-free rank two cluster algebras associated with
the matrix $\left(\begin{array}{cc} 0 & c\\-c & 0 \end{array}\right)$, and show
that a large number of coefficients are non-negative. As a corollary, we obtain
an explicit expression for the Euler-Poincar\'{e} characteristics of the
corresponding quiver Grassmannians.Virtual Private Overlays: Secure Group Commounication in NAT-Constrained Environments.
Mon, 01/18/2010 - 16:01 — SomNambulAuthors: Kyungyong Lee, David Isaac Wolinsky, Tae Woong Choi, P. Oscar Boykin, Renato Figueiredo
Subjects: Networking and Internet Architecture
AbstractStructured P2P overlays provide a framework for building distributed
applications that are self-configuring, scalable, and resilient to node
failures.Notes on a minimal set of generators for the radical ideal defining the diagonal locus of $(\C^2)^n$.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Kyungyong Lee, Li Li
Subjects: Combinatorics
AbstractWe develop several techniques for the study of the radical ideal $I$ defining
the diagonal locus of $(\C^2)^n$. Using these techniques, we give combinatorial
construction of generators for $I$ of certain bi-degrees.Notes on a minimal set of generators for the radical ideal defining the diagonal locus of $(\C^2)^n$.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Kyungyong Lee, Li Li
Subjects: Combinatorics
AbstractWe develop several techniques for the study of the radical ideal $I$ defining
the diagonal locus of $(\C^2)^n$. Using these techniques, we give combinatorial
construction of generators for $I$ of certain bi-degrees.$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Kyungyong Lee, Li Li
Subjects: Combinatorics
AbstractLet $I$ be the ideal generated by alternating polynomials in two sets of $n$
variables. Haiman proved that the $q,t$-Catalan number is the Hilbert series of
the graded vector space $M(=\bigoplus_{d_1,d_2}M_{d_1,d_2})$ spanned by a
minimal set of generators for $I$. In this paper we give simple upper bounds on
$\text{dim}M_{d_1, d_2}$ in terms of partition numbers, and find all bi-degrees
$(d_1,d_2)$ such that $\dim M_{d_1, d_2}$ achieve the upper bounds. For such
bi-degrees, we also find explicit bases for $M_{d_1, d_2}$.
User login
