(´ëÇѼöÇÐȸ Àü»ê¼öÇÐ ºÐ°ú 2001 ÇмúȸÀÇ)

 

KOREA COMBINATORICS, GRAPH THEORY,

ALGORITHMS and MATRIX THEORY SYMPOSIUM 2001

FEB., 20 - 21, 2001  POSTECH, POHANG, KOREA

 

 

  

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                     12½Ã 20ºÐ - 12½Ã 30ºÐ       :  Æä   ȸ

 

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(SESSION)

 

(20ÀÏ)

 

1. °ûÁøÈ£*, I. P. Goulden(Æ÷Ç×°ø´ë), ÀÌÀç¿î(¿µ³²´ë) : Distributions of  regular branched surface coverings

2. ¹ÚÁøÈ«*(¼±¹®´ë) :  How do we analyze Algorithms ?   

3. Á¶ÇÑÇõ(¼­¿ï´ë), ±è¼­·É(°æÈñ´ë)*, ³²À±¼ø(»ï¼º°íµî¿¬±¸¿ø) :  On m-step competition graphs,

4. ¹æ¼¼Á¤*, ¼Û¼º·Ä, Mitsugu Hirasaka(Æ÷Ç×°ø´ë) : Semidirect products of association schemes.

5. ÀÌ»ó¿í*, °í¿µ¹Ì(¼ö¿ø´ë) : Spectral Properties of Bipartite Tournament Matrices

6. ÀÌâ¿ì(¼­¿ï½Ã¸³´ë) : The Expected Independent Domination Number of a  Random Recursive Tree

7. ¼ÛÁØÈ£(¼­¿ï½Ã¸³´ë) : On Self-Avoiding Walks

8. Shao-Fei Du*, Jin Ho Kwak, Roman Nedela(Æ÷Ç×°ø´ë) : Regular embeddings of complete multipartite graphs

 

(21ÀÏ)

 

1. ¼Û¼º·Ä*(Æ÷Ç×°ø´ë), Kyoungah See, J. Stufken : Certain Combinatorial Block Designs and Spatially Constrained Sampling

2. ¼Û¼®ÁØ(Á¦ÁÖ´ë) : Linear operators preserving maximal column ranks of nonbinary Boolean matrices

3. ¼Õ¹«¿µ(â¿ø´ë) : Some connectivity of covering graphs

4. Á¶¼ºÁø(ºÎ°æ´ë)*, ±èÇѵÎ(ÀÎÁ¦´ë), ÃÖÀº¼÷(ºÎ°æ´ë) : Trees in linear nongroup cellular automata

5. ±èÁøȯ(¿µ³²´ë) : Embeddings of line graphs

6. ±èÁÖ¿µ(´ëÈ¿Ä«´ë) : The pebbling number of some graphs

7. ¹é¿µ±æ(ºÎ°æ´ë) : Applications of pictures in group presentation theory.

8. ±è°ü¼ö(¿µ³²´ë) : On outer automorphism groups of pinched 1-relator groups

9. ÀÌ»ó±¸(¼º±Õ°ü´ë) : A representation and some properties for k-Fibonacci sequences

 

 

 

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 °ûÁøÈ£*, I. P. Goulden, ÀÌÀç¿î (30ºÐ)

 

 ¹ÚÁøÈ«(30ºÐ)

    3:00-3:10    Tea Time

 Á¶ÇÑÇõ, ±è¼­·É*, ³²À±¼ø (20ºÐ)

 

 ¹æ¼¼Á¤*, ¼Û¼º·Ä, Mitsugu  Hirasaka(20ºÐ)

 

  ÀÌ»ó¿í*, °í¿µ¹Ì (20ºÐ)

    4:10-4:20 Tea Time

 ÀÌâ¿ì (20ºÐ)

 

 ¼ÛÁØÈ£ (20ºÐ)

 

 Shao-Fei Du*, Jin Ho Kwak, Roman Nedela (20ºÐ)

 

 

  

 

 

 

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  ¼Û¼º·Ä*, ½Ã°æ¼÷, J. Stufken (20ºÐ)

 

  ¼Û¼®ÁØ (20ºÐ)

 

 ¼Õ¹«¿µ (20ºÐ)

      10:00-10:10    Tea Time

 Á¶¼ºÁø*, ±èÇѵÎ, ÃÖÀº¼÷ (20ºÐ)

 

 ±èÁøȯ (20ºÐ)

 

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       11:10-11:20    Tea Time

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  12:20¡­12:30

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  14:00¡­16:30

  OPEN

 

 

 

 

 

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(2¿ù 20ÀÏ)

 

1. Jin Ho Kwak with I.P. Goulden and Jaeun Lee

Á¦ ¸ñ : Distributions of  regular branched surface coverings

ÃÊ ·Ï : In a study of surface branched coverings, one

can ask naturally:

In how many different ways can a given surface be a branched covering of another given surface?  In this paper, as a complete answer of the question for regular coverings, we  determine  the distribution of the regular branched coverings of any orientable or nonorientable surface when the covering transformation group and a set of branch points are fixed.

 

2. ¹ÚÁøÈ« (¼±¹®´ë)

Á¦ ¸ñ :  How do we analyze Algorithms?  

ÃÊ ·Ï : We shall discuss one of some techniques needed to analyze algorithms. It is called a big-O function technique.  The measures of efficiency of an algorithm

 have two cases. One is the {\it time } used by a computer to solve the problem using this algorithm when the input values are of a specified size.  The other one is the {\it amount of computer memory } required to implement the algorithm when the input values are of a specified size.

 

3. Á¶ÇÑÇõ(¼­¿ï´ë), ±è¼­·É*(°æÈñ´ë), ³²À±¼ø(»ï¼º°íµî¿¬±¸¿ø)

Á¦ ¸ñ : On $m$-step competition graphs

ÃÊ ·Ï : The competition graph of a digraph was introduced by Cohen in 1968associated with the study of ecosystems. Since then, the competition graph has been widely studied and many variations have been introduced.  Cho,~{\em et al.}~[1997] introduced the notion of $m$-step competition graph which is another generalization of competition graph.  If there is a directed walk of length $m$ from a vertex $x$ to a vertex $y$ in $D$, we call $y$ an $m$-step prey of $x$, and if a vertex $w$ is an  $m$-step prey of both vertices $u$ and $v$, then we say that $w$ is an $m$-step common prey of $u$ and $v$.The $m$-step competition graph of $D$,  denoted by $C^{m}(D)$, has  the same vertex set as $D$ and an edge  between vertices $x$ and $y$ if and only if $x$ and $y$ have an $m$-step common prey in $D$.  The $m$-step competition number $k^{(m)}(G)$ of $G$, which is the smallest number $k$ such that $G$ together with $k$ isolated vertices is the $m$-step competition graph of an acyclic digraph.

In this talk, we present  some main results on $m$-step competition graphs and $m$-step competition numbers.

 

4. ¹æ¼¼Á¤*, ¼Û¼º·Ä, Mitsugu Hirasaka(Æ÷Ç×°ø´ë)

Á¦ ¸ñ :  Semidirect products of association schemes

ÃÊ ·Ï : We construct a semidirect product of association sche-mes, and

derive a way to decompose a given association scheme into smaller

association schemes. We show that the semidirect product produces

many schemes that can not be described as the direct product nor

wreath product. We then investigate how much the semidirect

product helps us to understand and characterize the structure of

association schemes.

 

5. ÀÌ»ó¿í*, °í¿µ¹Ì(¼ö¿ø´ë)

Á¦ ¸ñ : Spectral Properties of Bipartite Tournament Matrices

ÃÊ ·Ï : A tournament is a complete digraph, that is, a complete graph with edges endowed with directions. The incidence matrix of a tournament is called a tournament matrix. In the same way, A bipartite tournament matrix is defined as the incidence matrix of a complete bipartite digraph, which is called a bipartite tournament, that is, a complete bipartite graph with edges directed. A bipartite tournament matrix is said to be of team size and if the underlying complete bipartite graph is .

        We look at the spectral bounds of a bipartite tournament matrix. Let be an irreducible bipartite tournament matrix with team size  . For an eigenvalue of , it is satisfied that ¡Â Re ¡Â . When the equality holds, the Perron value of should be with . We also find the condition for the variance of the Perron vector of the bipartite tournament matrix to vanish.        

 

 6. ÀÌâ¿ì(¼­¿ï½Ã¸³´ë)

Á¦ ¸ñ : The Expected Independent Domination Number of a Random Recursive Tree

ÃÊ ·Ï : We derive a formula for the expected value $\mu(n)$  of the independent domination number of a
random   recursive tree with $n$ vertices and show that the independent domination number of almost
every recursive tree with $n$ vertices is quite close to $n/2$.


 7. ¼ÛÁØÈ£(¼­¿ï½Ã¸³´ë)

Á¦ ¸ñ : On Self-Avoiding Walks

ÃÊ ·Ï : We investigate paths of a walker under the condition that the walker is not allowed to visit any point more than once and to make
any turn more than n\pi/2 from any of the direction previously taken on the square lattice.  Moreover, we study the properties of rational restriction in 2-choice, 3-choice directed self-avoiding walks, and \Phi_{max}=\pi model.  Using a graph theorical method, difference equations are derived to count the total number of paths of the walker.

 

 

8. Shao-Fei Du*, Jin Ho Kwak, Roman Nedela(Æ÷Ç×°ø´ë)

 

Á¦¸ñ : Regular embeddings of complete multipartite graphs

ÃÊ·Ï: TBA

 

(2¿ù 21ÀÏ)

 

1. ¼Û¼º·Ä*(Æ÷Ç×°ø´ë), Kyoungah See, John Stufken

Á¦ ¸ñ : Certain Combinatorial Block Designs and Spatially Constrained Sampling

ÃÊ ·Ï : In sampling, before selecting the sample, the population must be divided into parts called sampling units which have to cover the whole population and must not overlap. Sometimes the appropriate unit is obvious, other times there are several choices.  In sampling an agricultural crop or soil fertility, the unit might be a square region

of a field or an area of land. Suppose we have information that the neighboring units provide similar information about the population characteristics. In order to obtain better estimates of population characteristics, a researcher would like to take a sample which

does not include neighboring units simultaneously.  

  In this talk, we construct some designs, called polygonal designs especially useful for such a statistical sampling survey situation. We then demonstrate the use of the designs as such sampling plans. Our discussion will begin with the origin and background

idea of the problem. Then we construct designs appropriate for such sampling plans which avoid the selection of contiguous units. We will also look at a class of combinatorial block designs that are related to the sampling plans. Finally, we will discuss the existence and construction problems of such sampling plans in terms of

combinatorial block designs as well as further related research problems. If time permits we will see some examples that demonstrate the use of the combinatorial designs in practice.  

 

2.  ¼Û¼®ÁØ(Á¦ÁÖ´ë)

Á¦ ¸ñ : Linear operators preserving maximal column ranks of nonbinary Boolean matrices

ÃÊ ·Ï : The maximal column rank of an m by n matrix is maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.

 

3. ¼Õ¹«¿µ (â¿ø´ë)

Á¦ ¸ñ : Some connectivity of covering graphs

ÃÊ ·Ï :  In a study of covering graphs, one can ask the connectivity of covering graphs related with base graphs.  We will give some inequality of connectivity of covering graphs related with base graphs.

 

4. Á¶¼ºÁø(ºÎ°æ´ë)*, ±èÇѵÎ(ÀÎÁ¦´ë), ÃÖÀº¼÷(ºÎ°æ´ë)

Á¦ ¸ñ : Trees in linear nongroup cellular automata

ÃÊ ·Ï : We investigate the relationship between $0$-tree and other $\a(\not=0)$-tree in linear nongroup cellular automata.

 

5. ±èÁøȯ (¿µ³²´ë)

Á¦ ¸ñ : Embeddings of line graphs"

ÃÊ ·Ï :  For a 2-cell embedding of a graph $G$,  we

 consider a special 2-cell embedding for the line graph of G and

 a relationship between its lifts and covering graphs of $G$.

 

6. ±èÁÖ¿µ (È¿¼ºÄ«Å縯´ë)

Á¦ ¸ñ :  The pebbling number of some graphs

ÃÊ ·Ï :  Chung defined a pebbling move on a graph G to be
the removal of two pebbles from one vertex and the addition
of
one pebble to an adjacent vertex. The pebbling number of a
connected graph is the smallest number f(G) such that any
distribution of f(G) pebbles on G allows one pebble to be
moved to any specified, but arbitrary vertex. Graham conjectured
that for any connected graphs G and H,
f ( G product H ) < or = f(G) f(H).
We prove Graham's conjecture when G and H are fan graphs.


7. ¹é¿µ±æ(ºÎ°æ´ë)
Á¦ ¸ñ  : Applications of pictures in group presentation theory.

ÃÊ ·Ï  : TBA

8. ±è°ü¼ö(¿µ³²´ë)

Á¦ ¸ñ : On outer automorphism groups of pinched 1-relator groups

ÃÊ ·Ï :
Grossman showed that outer automorphism groups of
fundamental groups of closed orientable surfaces are residually finite.
Here we generalize her result by showing that outer automorphism
groups of generalized free products of two free groups amalgamating
a maximal cyclic subgroup are residually finite. From this it follows
that
mapping class groups of closed orientable and nonorientable surfaces
are residually finite. The latter answers a question raised by
A.M.~Gaglione.


 9. ÀÌ»ó±¸(¼º±Õ°ü´ë)

Á¦ ¸ñ : A representation and some properties for k-Fibonacci sequences

ÃÊ ·Ï : The  k-Fibonacci sequence, g_{n}^{(k)} is defined as  g_{1}^(k)  = cdots = g_{k-2}^{k)} = 0, g_{k-1}^(k)  = g_{k}^{k)} = 1  and for n > k >=2,

g_{n}^{(k)} = g_{n-1}^(k)  + g_{n-2}^{k)} + cdots + g_{n-k}^(k) . In this paper, we give a combinatorial representation of g_{n}^(k) and introduce some properties for k-Fibonacci sequence.

 

*****************

À̹ø Çмú ¸ðÀÓÀÇ ÃëÁö : Áö³­ ÇØ Ã¢¿ø´ë¿¡¼­ÀÇ ±¹Á¦ ÇмúȸÀÇ¿Í ³»³âÀÇ Àü»ê¼öÇבּ¸¼¾ÅÍ¿¡¼­ÀÇ  ±¹Á¦ÇмúȸÀÇ (INTERNATIONAL CONFERENCE on COMBINATORIAL MATRIX THEORY, Jan. 14 - Jan. 17, 2002, POSTECH, Pohang, Korea : °ø½Ä ȨÆäÀÌÁö:

http://math.skku.ac.kr/~sglee/postech/postech.htm) »çÀÌ¿¡ ±¹³»ÀÇ Àü»ê¼öÇÐ, Combinatorics, Graph Theory, Algorithms and Matrix Theory ºÐ¾ßÀÇ ¿¬±¸ ÀηÂÀÌ ¿ÃÇصµ Çѹø ¸¸³ª ¼­·ÎÀÇ ÀÇ°ßÀ» ±³È¯ÇÏ´Â ÀÚ¸®¸¦ ¸¶·ÃÇÑ´Ù´Â ÃëÁö·Î À̹ø ¹æÇÐÁß¿¡ ¸ðÀÓÀ» ¸¶·ÃÇß½À´Ï´Ù.

***************

CONFERENCE THEME

Combinatorics, Graph Theory,  Algorithms, Combinatorial Matrix Theory and related areas of Computational Mathematics.

 

OBJECTIVE :

Çѱ¹³»ÀÇ Combinatorics,Graph Theory, Algorithms and Matrix Theory ºÐ¾ßÀÇ °ü½ÉÀ»

Àç°íÇÏ°í, °øµ¿°ü½É»ç¿¡ °üÇÑ Á¤º¸±³È¯ ¹× ¿ìÈ£ÁõÁøÀ» À§ÇÏ¿©, ÃÖ¼Ò 1³â¿¡ ÇѹøÀº ¸¸³²ÀÇ ÀåÀ» ¸¶·ÃÇÑ´Ù´Â ÃëÁö·Î °ü½É ÀÖ´Â ¿¬±¸ÀÚµéÀÇ ¿¬±¸°á°ú ¹× ÁøÇà»çÇ×ÀÇ ¹ßÇ¥, ±³È¯ÇÏ´Â ÀåÀ» ¸¶·ÃÇÏ¿© ´õ¿í ¹ßÀüµÈ ¿¬±¸ ȯ°æÀ» ¸¸µå´Âµ¥ ³ë·ÂÇÑ´Ù.

 

CONFERENCE  

*Chair : °ûÁøÈ£(Æ÷Ç×°ø°ú´ë)

*Organizer : ¼Õ¹«¿µ(â¿ø´ë), ÀÌ»ó±¸(¼º±Õ°ü´ë)

 

EXCURSION
An excursion to Kyongju is possible.  Kyungju was the capital of Shilla Kingtom (57 BC - 935 AD) and  is Korea's tourist Meca.  The cost for the excursion including transportation, entrance fees, and dinner is about US$50.       
Nearby Attractions


ACCOMODATION
Space in a high class hotel has been reserved for participants at a discount rate.   The University Guest house,Young-Il Dae, and dormitory rooms of POSTECH are available to participants at much lower rate. You may visit the web site of the conference for reservation. (Details will be added)

 Pohang Culture &Public Information section (+82-562-245-6062,  6616)

City : http://city.pohang.kyongbuk.kr/english/f-introduce.htm

University : http://www.postech.ac.kr/e/

Housing : http://www.postech.ac.kr/e/guide_page/housing_related_services.html

 

 Local Information for Visitors:

Local Travel:  

Province Info  http://www.kyongbuktour.or.kr/eng/index.html

City Info. http://city.pohang.kyongbuk.kr/english/f-introduce.htm

More to come ...

 

International Travel & Visas:
Visitors to Korea from some countries require visas. If you are in doubt, please contact the Korean Consulate
http://www.koreanconsulate.org/eindex.htm nearest you. .

 

About Korea:

Please Visit the cite  "KOREA".

 

Next Meeting Announcement:

  

INTERNATIONAL CONFERENCE  

on

COMBINATORIAL MATRIX THEORY

Jan. 14 - Jan. 17, 2002

POSTECH, Pohang, Korea

 

Next CONFERENCE's Official WEB PAGE

The web site of the conference contains up-to-date information including electronic forms for submission of individual presentations.

http://matrix.skku.ac.kr/sglee/postech/postech.htm

 

 

 È«º¸ ´ë»ó : ´ëÇѼöÇÐȸ¿¡ °ü·Ã ¿¬±¸ÀηÂÀ¸·Î °ø½ÄÀûÀ¸·Î µî·ÏµÈ ¾Æ·¡ ºÐµé (ȸ¿ø¸íºÎ¿¡¼­ Combinatorics, Graph Theory, Algorithms, Matrix Theory ¿Í °ü·ÃµÈ ȸ¿ø ¸í´ÜÀ» °Ë»öÇÏ¿© ÀÌ-¸ÞÀÏ·Î ¾Æ·¡ºÐ¿¡°Ô ÃÊ´ëÀåÀ» º¸³Â½À´Ï´Ù. )

 

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