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\section{RESEARCH EXPERIENCE}
My previous experience involves working in various educational and research 
institutions including five universities, the three mentioned on the first page 
of this document, the University of Northern British Columbia (my current 
working place),  
 and the Technical University of Gabrovo, Bulgaria
where I worked from 1989 to 1993. 
I entered the Technical University with the rank of Assistant Professor after 
winning an academic competition.
While I was working there I was involved in a group called the Young 
Researchers Group. Our responsibilities were, among other things, to contribute 
to the development of a new series of textbooks called Mathematics for 
Engineering Education. I am a coauthor of two of these books.
During my stay at the Technical University of Gabrovo I became interested
in Design Theory. Shortly after that, in 1993, I came to Canada to continue my 
studies at the University of Victoria, and later
at Simon Fraser University. Currently, I am an Assistant Professor at the
University of Northern British Columbia.


My recent research is reflected in the articles listed in the publications 
section, 
as well as in my M.Sc. and Ph.D. theses; noting that most of the results of my 
M.Sc and Ph.D. theses have been published
in refereed journals. During my work experience I have collaborated and 
exchanged information with many other researchers, mostly via Internet or 
conference activities. I spent a year as a postdoctoral research fellow with 
professor K. Heinrich at Simon Fraser University. At that time, I was 
coordinating the meetings
of the Discrete Mathematics Seminar, communicating with other researchers and 
giving talks myself.

I will briefly discuss some of the most significant results of my research. 
This discussion includes a description of work in both Ph.D. and M.Sc. theses as 
well as some important results beyond the doctoral dissertation.
First, let me introduce some basic terms and notation.
Let $D$ = $\{ B_1, B_2,..., B_b \}$ be a finite
family of $k$-subsets (called {\bf blocks} of a $v$-set $X(v)$ = $\{ 1, 2,..., 
v \}$ 
(with elements called {\bf points}. Then $D$ is a $t$-$(v,k,\lambda )$ {\bf  
design} 
if every $t$-subset of $X(v)$ is contained in exactly $\lambda$ blocks of $D$.
If every $t$-subset of $X(v)$ is contained in at least $\lambda$ blocks of $D$, 
then  $D$ is a $t$-$(v,k,\lambda )$ {\bf  covering design} (or {\bf covering}. 
The number of blocks $b$ is the {\bf size} of the covering, and the minimum size 
of a $t$-$(v,k,\lambda )$ covering is called the {\bf covering number}, denoted 
$C_{\lambda }(v,k,t)$. A covering of size $C_{\lambda }(v,k,t)$ is called a {\bf 
minimal covering}. Let $D$ be a $t$-$(v,k,\lambda)$ design 
and $p =\max_{1\leq i<j\leq b} |B_i\cap B_j|.$
Let $p^*=min\; p$, where the minimum is taken over all designs with the same 
parameters.
Designs for which $p=p^*$ are called {\bf designs with maximally 
different blocks} (DMDB's).


The paper ~\cite{6} is concerned with new constructions of coverings.
There is no general theory behind obtaining good coverings. The existing 
computer algorithms produce coverings of poor quality in a reasonable
amount of time or coverings of good quality 
 but at a very large cost (CPU time).
Coverings with $v \leq 32 $ can be directly applied, for example, in 
error-trapping decoding. Since the complexity of the decoding procedure
depends on the size of the covering we are interested in finding coverings of 
minimum size  or if that is not possible, coverings of size as small as 
possible.
There are important applications of coverings in computer science--data 
compression and file organization schemes. Producers of lottery software are 
also interested in coverings. Recently, coverings have been applied in 
cryptography.
An interesting ``competition" started in 1993 when Nurmela and  
\"{O}sterg{\aa}rd published good coverings for $v \leq 13$ obtained by 
simulated annealing. This method also produces some good results 
for $v \geq 14$, but is quite time consuming. In 1995, Gordon, Kuperberg and 
Patashnik tabulated known results and expanded the tables to $v \leq 32$ and 
$t\leq 8$ using less precise, but faster algorithms. The same year Chang, Etzion 
and Wei published a paper in which they improve some of the results in Gordon et 
al. by using combinatorial constructions based on previous results of Etzion.
In ~\cite{6} we improve many of the bounds in those papers. 
The significance of our paper is that it provides many constructions for 
coverings which have smaller size than those currently being obtainable by 
computer methods. 
Most of the improvements are achieved by purely combinatorial arguments,
while others are assisted by computer searches. 
In the process of writing the final draft of this paper I contacted other 
researchers asking if they could suggest any improvements, similar results or
alternative solutions. H. H{\"a}m{\"a}l{\"a}inen responded with  
additional results and he became a coauthor. The paper was written entirely by 
me, according to suggestions from H. H{\"a}m{\"a}l{\"a}inen, K. Heinrich, T. 
Etzion, and
the referees.

In ~\cite{5} I found three new families of minimal $(t+1)$-coverings obtained 
from 
$t$-designs. The coverings produce new covering numbers for an infinite number 
of parameters. Aside from $t$-designs (which are also t-coverings) prior to this
work only three infinite families of coverings with $t\geq 3$ were known, those 
obtained by Ray-Chaudhuri in 1968,
Abraham, Ghosh and Ray-Chaudhuri in 1968, and Todorov in 1984. 


Designs are used in statistical planning of experiments.
In ~\cite{1}, an extension theorem for $t$-designs is proved. As an application,
a family of $4$-$(4^m+1,5,2)$ designs is constructed by extending
designs related to the 3-designs formed by the minimum weight vectors
in the Preparata code of length $n=4^m, \ m\geq 2$.
At that time, the only known construction of a $3$-$(16,6,4)$ design with $p=3$
was the one obtained from the Preparata codes. I found an alternative solution 
and used it to
construct the smallest representative of the new family, the $4$-$(17,5,2)$ 
design
$(m=2)$. I sent this construction to Tonchev at Michigan Technological 
University who
with Baartmans generalized it.
This
was the first example of an infinite family of designs with $t \geq 4$ and
constant $\lambda$. Recently, Bierbrauer found other examples, but
our family is still the only example of an infinite family of designs with 
$t\geq 4$ obtained from codes. It is also the only family of designs with the 
smallest $\lambda$ possible for a design with repeated blocks. Note that a  
$4$-$(4^m+1,5,2)$ design without repeated blocks is not known to exist
even in the smallest case $m=2$.

In ~\cite{2} we introduce a new method for finding designs and use it to study 
the 
existence of designs with maximally different blocks. The paper ~\cite{3} is a 
continuation of ~\cite{2}. In addition to the method described in ~\cite{3} we 
employ 
variations on the greedy algorithm for finding designs and partitions of a 
$t$-design into
$(t-1)$-designs.
In ~\cite{4} we investigate the intersection number of known designs. We prove 
that 
designs obtained from codes in works of Assmus and Matson, and MacWilliams, 
Odlyzko and Sloan are designs with small intersection number. We then use a 
result of Driessen and a previously unknown corollary to this result to prove 
the existence of over 500 new 3,4, and 5-designs.
In ~\cite{7} we combine methods from ~\cite{4} and ~\cite{3} with the proof that 
a design obtained 
from a code of van Lint and MacWilliams is a design with small intersection 
number
to prove the existence of new 3-designs. Part of the designs are obtained
from the inversive geometry of order 5 via a method described in ~\cite{3} and 
~\cite{2}.
 
In a recent joint paper with M. Greig and K. Heinrich ~\cite{11} 
we find new infinite classes of covering numbers. Some of the classes depend on 
two or three different parameters, so any particular value of one of the 
parameters produces a separate infinite class thus resolving the existence of 
minimal  coverings for quite a wide spectrum of parameters.
Postscript files of recent papers can be found at my web-site (see the beginning 
of this document). In March, 1998 I was invited at the University of Nebraska
by Spyros Magliveras and Douglas Stinson to give talks on coverings, and to work 
on large sets of designs. This visit resulted in the joint paper ~\cite{10}. I 
have 
also 
colaborated with K. Heinrich on two other papers, ~\cite{9} and ~\cite{8}. In 
~\cite{8} we found
some further generalizations of the results from ~\cite{6}. The paper ~\cite{9} 
complements
the works of other researchers on super-simple designs.

Recently I became interested in combinatorial optimization and the possibilities
of using combinatorial optimization as a computational tool for solving problems
in various areas of discrete mathematics. 
Some of the results in ~\cite{6}, ~\cite{12} and ~\cite{13} were found by 
optimization. These 
works 
gave me the opportunity to study the existing optimization methods, compare 
their performance, notice some common weaknesses of these methods and 
eventually develop a new method that overperforms (and generalizes) all of the 
existing methods. I call it a Level Dependent Experimental Optimization.
The potential of the new method has been exploited, among other tools, in 
several new works (still
in progress), for example, a couple of joint works (with Abel and Greig) on 
BIBD's and a singly authored paper on double coverings. 
 
 I am fascinated
by the object of my studies and research and have many ideas for future
projects and experiments. Needless to say, I am always trying to see the 
applications of what I am doing, or, alternatively, to look for solutions of 
practical problems.
 I believe that I have very good organizational skills, and I am able to 
conduct and supervise research, collaborate with other researchers, and 
communicate the results successfully to a broader audience.
 I also believe that I will be able to make other valuable contributions to the 
Mathematical Science in the future.


\section{FUTURE RESEARCH PLANS}


Coverings have applications in communications and computer science via 
error trapping decoding 
and data compression, respectively, and in coding theory. Recently, coverings 
have been used in cryptography. I am interested in 
constructing coverings that improve the known upper bounds on the corresponding 
covering numbers. I will search for various types of designs with certain 
extremal properties that can be used to produce other combinatorial structures; 
coverings in particular. These include partially balanced designs, group 
divisible designs and designs with maximally different blocks. I would like to 
explore 
some interconnections between design theory and other areas
of mathematics, for example, algebra, graph theory, coding theory and finite 
geometries.

I am planning to continue the search for good coverings (coverings with the
smallest possible size). I believe that some other general constructions can be
obtained once we have good knowledge on the properties and structure of small 
coverings. There is a possibility of applying
GAP (Groups Applications Package) of RWTH-Aachen and  
Discreta of Betten, Laue and Wassermann in the searches.
The first two 
packages can be used to generate appropriate groups. It will be generally 
difficult to improve the covering
bounds in the current range of applications. The bounds have been recently 
attacked by 
several computer searches via optimization
acting on the set of all $k$-subsets. One possible alternative that
I want to explore is experimenting with optimization algorithms
acting on the set of representatives of orbits on the $k$-sets under the action
of a prescribed group of automorphisms of the covering. The success
of a computer search for minimal coverings would allow us to look
at the structure of these coverings and possibly find other general
direct combinatorial constructions.


Many of the known construction of combinatorial objects are 
based on properties of geometry structures.
I am particularly interested in finding new applications of finite geometry in 
the constructions of coverings, packings and designs.


Recently I have developed a powerful optimization method which I want to try in 
various searches for designs and other combinatorial structures. I would also 
want to look 
at the possibility of using the idea of the method in continuous 
optimization.

\begin{thebibliography}{32}
\bibitem{1} A.H.Baartmans, I.D.Bluskov, V.D.Tonchev, The Preparata Codes and
a Class of 4-Designs, Journal of Combinatorial Designs, vol.2, No.3
(1994), 167-170.
\bibitem{2} I. Bluskov, Designs with Maximally Different Blocks, Utilitas 
Mathematica, 
 48 (1995), 193-201. 
\bibitem{3} I. Bluskov, Designs with Maximally Different Blocks and $v=15,16$, 
Utilitas Mathematica, 50(1996), 203-213. 
\bibitem{4} I. Bluskov, New Designs, Journal of Combinatorial Mathematics
and Combinatorial Computing, 23(1997), 212-220. 
\bibitem{5} I. Bluskov, Some $t$-Designs are Minimal $(t+1)$-Coverings, Discrete 
Mathematics 188(1998), 245-251.  
\bibitem{6} I. Bluskov, Heikki H{\"a}m{\"a}l{\"a}inen, New Upper Bounds on the 
Minimum 
Size of Covering Designs, Journal of Combinatorial Designs, vol.6, No.1
(1998), 21-41. 
\bibitem{7} I. Bluskov, New Simple 3-Designs on 26 and 28 Points, Ars 
Combinatoria 
51(1999), 313-318.
\bibitem{8} I. Bluskov and K. Heinrich, General Upper Bounds on The Minimum Size 
of 
Covering Designs, Journal of Combinatorial Theory, Series A, 86(1999), 205-213. 
\bibitem{9} I. Bluskov and K. Heinrich, Super-simple designs with $v\leq 32$, 
accepted 
for
publication in Journal of Statistical Planning and Inference, July 9, 1998. 
\bibitem{10} I. Bluskov and S. Magliveras, On the Number of Mutually Disjoint 
Cyclic
Designs and Large Sets of Designs, accepted for
publication in Journal of Statistical Planning and Inference, June 22, 1998. 
\bibitem{11} I. Bluskov, M. Greig and K. Heinrich, Infinite Classes of Covering 
Numbers, accepted in Canadian Mathematical Bulletin, Oct. 21, 1999.
\bibitem{12} I. Bluskov, Optimization Algorithms and Cyclic Designs,
Journal of Geometry, 67(2000), 42-49.
\bibitem{13} J. Abel, I. Bluskov, M. Greig,
Balanced Incomplete Block Designs with Block Size 8, accepted for publication in 
Journal of Combinatorial Designs, July 2000.
\end{thebibliography}
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