Posts Tagged ‘김장수’

Jang Soo Kim (김장수), New Interpretations for Noncrossing Partitions of Classical Types

Monday, January 11th, 2010
New Interpretations for Noncrossing Partitions of Classical Types
Jang Soo Kim (김장수)
Laboratoire d’Informatique Algorithmique: Fondements et Applications (LIAFA), University of Paris 7, France
2010/1/21 Thu 4PM-5PM

The Catalan number \(\frac{1}{n+1}\binom{2n}{n}\) is perhaps the most frequently occurred number in combinatorics. Richard Stanley has collected more than 170 combinatorial objects counted by the Catalan number. Noncrossing partition, which has received great attention recently, is one of these, so called, Catalan objects. Noncrossing partitions are generalized to each finite Coxeter group. In this talk, we will interpret noncrossing partitions of type B in terms of noncrossing partitions of type A. As applications, we can prove interesting properties of noncrossing partitions of type B.

Jang Soo Kim (김장수), A combinatorial approach to the power of 2 in the number of involutions

Friday, December 5th, 2008
A combinatorial approach to the power of 2 in the number of involutions
Jang Soo Kim (김장수)
Dept. of Mathematical Sciences, KAIST, Korea.
2008/12/11 Thu, 5:30PM-6:30PM
We prove combinatorially that the largest power of 2 in the number of involutions of length n is equal to [n/2]-2[n/4] +[(n+1)/4]. We show that the smallest period of the sequence of odd factors in the number of involutions modulo 2s is 2s+1 for s>2. We also consider the largest power of 2 in the number of even and odd involutions.