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Contributed Papers Session / Communications libres
(Org: To be announced)
- MAJID BEHBAHANI, University of Lethbridge, Lethbridge, Alberta
An exhuastive search for orthogonal designs of small order
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We show that OD(12;1,1,1,9) is the only orhtogonal design of
order 12 constructible from 16 circulant matrices.
- TCHAVDAR MARINOV, Department of Mathematical Sciences, University of Alberta
Edmonton, Alberta T6G 2G1
Identification the heat-conduction coefficient via method of
variational imbedding
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Following the main idea if MVI the inverse parabolic problem of
coefficient identification from over-posed data is imbedded into a
quadratic functional from governed equation. The necessary condition
for minimization of the functional (the Euler-Lagrange equations)
comprise a fourth-order in space and second-order in time elliptic
boundary value problem for the temperature and a second-order in space
ODE for the unknown coefficient.
The imbedding problem is well-posed for redundant data at boundaries
and possesses a unique solution which means that when the imbedding
functional is zero, the over-posed data is consistent and the solution
of the imbedding problem coincides with the sought solution of the
inverse problem.
A difference scheme of splitting type is employed and featuring
examples are elaborated numerically. The numerical results confirm that
the solution of the imbedding problem coincides with the direct
simulation of the original problem within the truncation error
O(t2+h2).
- ARIANE MASUDA, School of Mathematics and Statistics, Carleton University,
Ottawa, Ontario K1S 5B6
A characterization of permutation polynomials based on
their coefficients
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This is joint work with D. Panario (Carleton University) and S. Q. Wang
(University of Lethbridge).
We give a characterization of permutation polynomials over a finite
field Fq based on their coefficients. As a result, explicit
conditions for a polynomial to be a permutation polynomial are given
when q=2, 3, 5. Moreover, permutation binomials over
Fq are completely described. New classes of permutation
binomials and polynomials can be constructed accordingly.
- JUSTIN MAUGER, Whittier College, Whittier, California 90608, USA
The cohomology of certain Hopf algebras associated
with p-groups
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We study the cohomology H*(A)=ExtA*(k,k) of a locally finite,
connected, cocommutative Hopf algebra A over k=Fp. Specifically, we
are interested in those algebras A for which H*(A) is generated as
an algebra by H1(A) and H2(A). We shall call such algebras
semi-Koszul. Given a central extension of Hopf algebras F®A® B with F monogenic and B semi-Koszul, we use the
Cartan-Eilenberg spectral sequence and algebraic Steenrod operations to
determine conditions for A to be semi-Koszul. Special attention is
given to the case in which A is the restricted universal enveloping
algebra of the Lie algebra obtained from the mod-p lower central
series of a p-group. We show that the algebras arising in this way
from extensions by Z/(p) of an abelian p-group are semi-Koszul.
Explicit calculations are carried out for algebras arising from rank 2
p-groups, and it is shown that these are all semi-Koszul for p ³ 5.
- KAREN MEAGHER, Department of Mathematics and Statistics, Unversity of Ottawa,
Ottawa, Ontario K1N 6N5
Covering arrays on graphs
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Two vectors v, w on Zg are vector independent if
for all pairs (a, b) Î Zg ×Zg there is a
position i in the vectors where (a,b) = (vi,wi). A covering array
on a graph G, denoted CA(G,g), is an array on Zg with
|V(G)| rows and the property that any two rows which correspond to
adjacent vertices in G are vector independent. We define a family of
graphs G(n,g) whose vertices are length n vectors on Zg
and edges join two vertices if they are vector independent. A graph G
has a covering array with n columns if and only if there is a
homomorphism from G to G(n,g). Hence, finding a covering array on a
graph is similar to finding the chromatic number, the r chromatic
number or the star chromatic number of a graph.
- MARNI MISHNA, LaCIM, Université du Québec à Montréal
A holonomic approach to combinatorics
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The vector space of symmetric functions possesses a well-known scalar
product which has a variety of combinatorial applications. This scalar
product has been used to express generating functions of combinatorial
objects, and often one can determine conditions for when these series
are D-finite. That is, when do such series satisfy a differential
equation with polynomial coefficients? We extend earlier work by
providing algorithms that compute the differential equations these
generating functions satisfy.
This talk will outline the fundamentals of the so called holonomic
approach to combinatorics. The principal algorithms compute the
differential equations satisfied by images of (series of) symmetric
functions under different maps; Notably the aforementioned scalar
product, the tensor (or Kronecker) product (linked to the computation
of certain characters) and various q-analogs. The algorithms use
Groebner bases in non-commutative algebras, and are implemented in
Maple.
Finally, we will present a host of examples from enumerative
combinatorics well suited to this approach: regular graphs, plane
partitions, latin squares, Young tableaux,...
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