Peter Sin
The Elementary Divisors of the Incidence Matrices of Skew Lines in PG(3,p).
Fri, 01/15/2010 - 16:01 — SomNambulAuthors: Peter Sin, Joshua Ducey
Subjects: Combinatorics
AbstractThe elementary divisors of the incidence matrices of lines in $PG(3,p)$ are
computed, where two lines are incident if and only if they are skew.Dimensions of Some Binary Codes Arising From A Conic in $PG(2,q)$.
Thu, 11/12/2009 - 16:01 — SomNambulAuthors: Peter Sin, Junhua Wu, Qing Xiang
Subjects: Combinatorics
AbstractLet $\mathcal{O}$ be a conic in the classical projective plane $PG(2,q)$,
where $q$ is an odd prime power. With respect to $\mathcal{O}$, the lines of
$PG(2,q)$ are classified as passant, tangent, and secant lines, and the points
of $PG(2,q)$ are classified as internal, absolute and external points. The
incidence matrices between the secant/passant lines and the external/internal
points were used in \cite{keith1} to produce several classes of structured
low-density parity-check binary codes.The Divisor Matrix, Dirichlet Series and SL(2,Z), II.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Peter Sin, John G. Thompson
Subjects: Number Theory
AbstractWe examine an elliptic curve constructed in an earlier paper from a certain
representation of $\SL(2,\Z)$ on the space of convergent Dirichlet series. The
curve is observed to be a modular curve for $\Gamma^1(15)$ and a certain orbit
of modular functions is thereby associated with the Riemann zeta function.
Explicit descriptions are given of these functions and of the permutation
action of $\SL(2,\Z)$ on them.Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Ogul Arslan, Peter Sin
Subjects: Representation Theory
AbstractWe determine the characters of the simple composition factors and the
submodule lattices of certain Weyl modules for classical groups. The results
have several applications. The simple modules arise in the study of incidence
systems in finite geometries and knowledge of their dimensions yields the
$p$-ranks of these incidence systems.
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