A Gray path on binary partitions (2009)
Colthurst, Thomas, Kleber, Michael
A binary partition of a positive integer $n$ is a partition of $n$ in which each part has size a power of two. In this note we first construct a Gray sequence on the set of binary partitions of $n$....
Abstract. We exhibit a “method ” for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi–Trudi identity. We illustrate this...
Mathematical Exposition (2008)
Combinatorics in representation theory: symmetric functions and Lie groups (05E05/10/15, 05A10 17B10), especially quantum affine algebras (05A30, 17B37) Effective computation and computational...
Tournament sequences and Meeussen sequences, Electron (2008)
A tournament sequence is an increasing sequence of positive integers (t1,t2,...) such that t1 =1andti+1 ≤ 2ti. AMeeussen sequence is an increasing sequence of positive integers (m1,m2,...) such...
ALLPATHS: De novo assembly of whole-genome shotgun microreads (2008)
Butler, Jonathan, MacCallum, Iain, Kleber, Michael, Shlyakhter, Ilya A., Belmonte, Matthew K., Lander, Eric S., ...
New DNA sequencing technologies deliver data at dramatically lower costs but demand new analytical methods to take full advantage of the very short reads that they produce. We provide an initial,...
Polynomial Relations Among Characters coming from Quantum Affine Algebras (2007)
The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of gl n. Earlier work of Kirillov and Reshetikhin proposed a generalization of these...
Linearly Independent Products of Rectangularly Complementary Schur Functions (2007)
Fix a rectangular Young diagram R, and consider all the products of Schur functions s s , where and run over all (unordered) pairs of partitions which are complementary with respect to R.
Linearly Independent Products of (2007)
Rectangularly Complementary Schur, Michael Kleber
Fix a rectangular Young diagram R, and consider all the products of Schur functions s # s # c ,where# and # run over all (unordered) pairs of partitions which are complementary with respect to R.
This "Mathematical Entertainments" column from the Intelligencer is an exposition of current investigations, rooted in recent work of Jim Propp, into "quasirandom" analogues of random walk and random...
Tensor product stabilization in Kac-Moody algebras (2004)
Kleber, Michael, Viswanath, Sankaran
We consider a large class of series of symmetrizable Kac-Moody algebras (generically denoted X_n). This includes the classical series A_n as well as others like E_n whose members are of Indefinite...
Increasing trees and Kontsevich cycles (2003)
Igusa, Kiyoshi, Kleber, Michael
It is known that the combinatorial classes in the cohomology of the mapping class group of punctures surfaces defined by Witten and Kontsevich are polynomials in the adjusted Miller-Morita-Mumford...
Linearly Independent Products of Rectangularly Complementary Schur Functions (2002)
Fix a rectangular Young diagram R, and consider all the products of Schur functions s(mu) s(mu^c), where mu and mu^c run over all (unordered) pairs of partitions which are complementary with respect...
Symmetric Functions and Representations of Quantum Affine Algebras (2000)
Chari, Vyjayanthi, Kleber, Michael
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations...
Embeddings of Schur functions into types B/C/D (2000)
We consider the problem of embedding the semi-ring of Schur-positive symmetric polynomials into its analogue for the classical types $B/C/D$. If we preserve highest weights and add the additional...
Tournament Sequences and Meeussen Sequences (2000)
Cook, Matthew, Kleber, Michael
A tournament sequence is an increasing sequence of positive integers (t1; t2; : : :) such that t1 = 1 and ti+1
Fulmek, Markus, Kleber, Michael
We present a ``method'' for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi--Trudi identity. We illustrate this ``method'' by...
Tournament Sequences and Meeussen Sequences (2000)
Cook, Matthew, Kleber, Michael
A "tournament sequence" is an increasing sequence of positive integers (t_1,t_2,...) such that t_1=1 and t_{i+1}
Plucker Relations on Schur Functions (1999)
We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of rectangular...
Polynomial Relations Among Characters coming from Quantum Affine Algebras (1999)
The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of $gl_n$. Earlier work of Kirillov and Reshetikhin proposed a generalization of these...
Finite Dimensional Representations of Quantum Affine Algebras (1998)
We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an...
We compute the decomposition of representations of Yangians into g-modules for simply-laced g. The decomposition has an interesting combinatorial tree structure. Results depend on a conjecture of...
We compute the decomposition of representations of Yangians into g-modules for simply-laced Lie algebras g. The decomposition has an interesting combinatorial tree structure. Results depend on a...
Rostock, Med. F., Diss. v. 2. Sept. 1969 (Nicht f. d. Aust.).
ALLPATHS: De novo assembly of whole-genome shotgun microreads
Butler, Jonathan, MacCallum, Iain, Kleber, Michael, Shlyakhter, Ilya A., Belmonte, Matthew K., Lander, Eric S., ...
New DNA sequencing technologies deliver data at dramatically lower costs but demand new analytical methods to take full advantage of the very short reads that they produce. We provide an initial,...