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The 1st KIAS Combinatorics Workshop was held at KIAS on November 8- 9, 2013.
- Date: November 8 - 9 (Fri-Sat), 2013
- Venue: Room 1503, KIAS
- Invited Speakers
Woong Kook (Seoul National University)
Sejeong Bang (Yeungnam University)
Heesung Shin (Inha University)
- List of Participants
- Schedule
[1st Day, November 8th]
14:00 ~ 14:50 <Talk 1> Woong Kook
- "Simplicial Tree Numbers for Matroid Complexes"
15:00 ~ 15:50 <Talk 2> Sejeong Bang - "Spectral characterization of distance-regular graphs
- with the smallest eigenvalue $theta_3geq-3$"
Coffee Break
16:20 ~ 17:10 <Talk 3> Heesung Shin - "Eulerian polynomials via continued fractions"
17:20 ~ 18:00 Problem session
18:00 ~ 20:00 Banquet - [2nd Day, November 9th]
- 09:00 ~ 10:00 Breakfast
- 10:00 ~ 12:00 Discussions
- Abstracts
- <Talk 1> Woong Kook
- "Simplicial Tree Numbers for Matroid Complexes"
- <Talk 2> Sejeong Bang
- "Spectral characterization of distance-regular graphs with the smallest eigenvalue $theta_3geq-3$"
- <Talk 3> Heesung Shin
- "Eulerian polynomials via continued fractions"
Using continued fraction expansion, it is shown that the sequence of coefficients of Eulerian polynomial is symmetric and unimodal. Recently, Blanco and Petersen (arXiv:1206.0803v2) conjectured a $q$-analogue of Eulerian polynomial as an expansion formula for inversions and excedances in the symmetric group. In this talk, we prove this conjecture.
Also, we can find a similar expansion for the eulerian polynomials of fixed-point free permutations of type B. This formula gives an answer to a conjecture of Mongelli (J. Combin. Theory Ser. A 120 (2013), no. 6, 1216–1234) about the unimodality of coefficients in the corresponding Eulerian polynomials.
- Problem Session