Archive for the ‘2012’ Category

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Seog-jin Kim (김석진), On-line list colouring of complete multipartite graphs

Wednesday, March 21st, 2012
On-line list colouring of complete multipartite graphs
Seog-Jin Kim (김석진)
Dept. of Mathematics Education, Konkuk University, Seoul, Korea.
2011/4/18 Wed 4PM-5PM
The well-known Ohba Conjecture says that every graph G with |V(G)|≤ 2χ(G)+1 is chromatic choosable.
This paper studies an on-line version of Ohba Conjecture. We prove that unlike the off-line case, for k≥3, the complete multipartite graph K2*(k-1), 3 is not on-line chromatic-choosable. Based on this result, the on-line version of Ohba Conjecture is modified as follows: Every graph G with |V(G)|≥ 2χ(G) is on-line chromatic choosable. We present an explicit strategy to show that for any positive integer k, the graph K2*k is on-line chromatic-choosable. We then present a minimal function g for which the graph K2*(k-1), 3 is on-line g-choosable. This is joint work with Young Soo Kwon, Daphne Der-Fen Liu, and Xuding Zhu.

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Posted in 2012, KAIST Discrete Math Seminar | Comments Closed

Meesue Yoo (유미수), p-rook numbers and cycle counting in the wreath product of Cp and Sn

Wednesday, February 29th, 2012
p-rook numbers and cycle counting in the wreath product of Cp and Sn
Meesue Yoo (유미수)
School of Mathematics, KIAS, Seoul, Korea
2012/4/4 Wed 4PM-5PM
The cycle counting rook numbers, hit numbers, and q-rook numberes and q-hit numbers have been studied by many people, and Briggs and Remmel introduced the theory of p-rook and p-hit numbers which is a rook theory model of the weath product of the cyclic group Cp and the symmetric group Sn.
We extend the cycle-counting q-rook numberes and q-hit numbers to the Briggs-Remmel model. In such a settinig, we define multivariable version of the cycle-counting q-rook numbers and cycle-counting q-hit numbers where we keep track of cycles of pernutation and partial permutation of Cp wearth product with Sn according to the signs of the cycles.
This work is a joint work with Jim Haglund at University of Pennsylvania and Jeff Remmel at UCSD.

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Posted in 2012, KAIST Discrete Math Seminar | Comments Closed

Byungchan Kim (김병찬), The Odd Moments of Ranks and Cranks

Tuesday, February 28th, 2012
The Odd Moments of Ranks and Cranks
Byungchan Kim (김병찬)
School of Liberal Arts, Seoul National University of Science and Technology, Seoul, Korea
2012/3/28 Wed 4PM-5PM
By modifying the definition of moments of ranks and cranks, we study the odd moments of ranks and cranks. In particular, we prove the inequality between the first crank moment M1(n) and the first rank moment N1(n):

M1(n) > N1(n).

We also study new counting function ospt(n) which is equal to M1(n) – N1(n). We will also discuss higher order moments of ranks and cranks.
This is a joint work with G. E. Andrews and S. H. Chan.

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Posted in 2012, KAIST Discrete Math Seminar | Comments Closed

HwanChul Yoo (유환철), Purity of weakly separated set families

Wednesday, February 22nd, 2012
Purity of weakly separated set families
HwanChul Yoo (유환철)
School of Mathematics, KIAS, Seoul, Korea
2012/3/14 Wed 4PM-5PM
Weakly separated set families were first studied by Leclerc and Zelevinsky in the context of quantum flag variety. Two quantum Plücker coordinates quasi-commute whenever their indexing sets are weakly separated. It was conjectured that maximal such families always have the same size. Similar question was asked by Scott when she studied quantum Grassmannian. These conjectures were independently proved by Danilov-Karzanov-Koshevoy and Oh-Postnikov-Speyer using some planar graphs and by the author using truncation. In this talk, definitions and motivations for the weakly separated set families will be explained, including Oh-Postnikov-Speyer’s point of view on the subject. The proof of the purity conjecture using truncation will be provided, and related questions will be discussed.

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Posted in 2012, KAIST Discrete Math Seminar | Comments Closed

Tony Huynh, Intertwining connectivities for matroids

Tuesday, February 21st, 2012
Intertwining connectivities for matroids
Tony Huynh
Department of Mathematical Sciences, KAIST
2012/2/29 Wed 4PM-5PM
An intertwine of two graphs G and H is a graph that has both G and H as a minor and is minor-minimal with this property. In 1979, Lovász and Unger conjectured that for any two graphs G and H, there are only a finite number of intertwines. This now follows from the graph minors project of Robertson and Seymour, although no ‘elementary’ proof is known.
In this talk, we consider intertwining problems for matroids. Bonin proved that there are matroids M and N that have infinitely many intertwines. However, it is conjectured that if M and N are both representable over a fixed finite field, then there are only finitely many intertwines. We prove a weak version of this conjecture where we intertwine ‘connectivities’ instead of minors. No knowledge of matroid theory will be assumed.
This is joint work with Bert Gerards (CWI, Amsterdam) and Stefan van Zwam (Princeton University).

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Posted in 2012, KAIST Discrete Math Seminar | Comments Closed

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