# Research

## Research interests

- Combinatorics,
*q*-series and special functions

## Publications

- (with Sen-Peng Eu and Seunghyun Seo) Enumerations of vertices among all rooted ordered trees with levels and degrees, arXiv:1605.00715, to appear in Discrete Mathematics, 2017.
- (with Jiang Zeng) Symmetric unimodal expansions of excedances in colored permutations, arXiv:1411.6184, European Journal of Combinatorics, 52, part A, 174-196, 2016. / MR3425973
- (with Seunghyun Seo) Signed a-polynomials of graphs and Poincaré polynomials of real toric manifolds, arXiv:1212.6307, Bulletin Korean Mathematical Society, 52(2), 467-481, 2015. / MR3338206
- (with Jang Soo Kim and Seunghyun Seo) Annular noncrossing permutations and minimal transitive factorizations, arXiv:1201.5703, Journal of Combinatorial Theory, Series A, 124, 251-262, 2014. / MR3176201
- (with Seunghyun Seo) A refinement for
*p*-ary labeled trees, arXiv:1311.7492, Korean Journal of Mathematics, 21(4), 495-502, 2013. - (with Seunghyun Seo) A refinement for ordered labeled trees, arXiv:1207.3291, Korean Journal of Mathematics, 20(2), 225-261, 2012.
- (with Jiang Zeng) The symmetric and unimodal expansion of Eulerian polynomials via continued fractions, arXiv:1005.4583, European Journal of Combinatorics, 33(2), 111-127, 2012. / MR2854634
- (with Seunghyun Seo) On the enumeration of rooted trees with fixed size of maximal decreasing trees, arXiv:1106.1290, Discrete Mathematics, 312(2), 419-426, 2012. / MR2852601
- (with Sohyun Hwang et al) Context-dependent transcriptional regulations between signal transduction pathways, BMC Bioinformatics 2011, 12:19, 2011.
- (with Yoann Gelineau and Jiang Zeng) Bijections for Entringer families, arXiv:1004.2179, European Journal of Combinatorics, 32(1), 100-115, 2011. / MR2727465
- (with Jiang Zeng) A bijective enumeration of labeled trees with given indegree sequence, arXiv:0805.0067, Journal of Combinatorial Theory, Series A, 118(1), 115-128, 2011. / MR2737188
- (with Jiang Zeng) The
*q*-tangent and*q*-secant numbers via continued fractions, arXiv:0911.4658, European Journal of Combinatorics, 31(7), 1689-1705, 2010. / MR2673011 - (with Jiang Zeng) An involution for symmetry of hook length and part length of partitions, arXiv:0907.4880, Discrete Mathematics, 310(10-11), 1633-1639, 2010. / MR2601273
- (with Seunghyun Seo) A generalized enumeration of labeled trees and reverse prüfer algorithm, arXiv:math/0601009, Journal of Combinatorial Theory, Series A, 114(7), 1357-1361, 2007. / MR2353128
- (with Manwon Cho et al) Colored prüfer codes for
*k*-edge colored trees, Electronic Journal of Combinatorics 11(1), N10, 2004. / MR2097341

## Conference Proceedings

- (with Jang Soo Kim and Seunghyun Seo) Minimal transitive factorizations of a permutation of type (p,q), FPSAC 2012, 2012. / PDF
- (with Jiang Zeng) A further correspondence between
*(bc,b)*-parking functions and*(bc,b)*-forests, FPSAC 2009, 2009. / DMTCS Proceedings AK, 793-804. - (with Seunghyun Seo) Two involutions on vertices of ordered trees, FPSAC 2002, 2002. / PDF

## Preprints

- (with Suyoung Choi) On a decomposition of simple polytopes, in preparation, 2010.
- A refined bijection between alternating permutations and
*0-1-2*increasing trees, arXiv:1003.4564, preprint, 2010. - A new bijection between forests and parking functions, arXiv:0810.0427, submitted, 2008.

## Talks

- Convolutional Neural Networks in Keras with CIFAR-10 dataset, Optimization and Learning Tutorial 2018, Ajou University, Suwon, Korea, March 31, 2018.
- Hot to use JupyterHub for mathematics, Math Colloquium, Inha University, Incheon, Korea, March 29, 2017.
- Welcome to Python and SageMath, SageMath Developers Meeting 2017, Sungkyunkwan University, Korea, Feb. 1, 2017
- Hot to use JupyterHub for data analysis, Setup of JupyterHub and its application, Korea University, Korea, Dec. 9, 2016.
- Enumerations of vertices among all rooted ordered trees with levels and degrees, The 12th KIAS Combinatorics Workshop, KIAS, Seoul, Korea, June 3, 2016. / silde
- Education and research by SageMath, Mathematical Software Working Seminar, Korea University, Seoul, Korea, June 12, 2015.
- Continued fractions and generalized Fibonacci numbers, 2014 Combinatorics Workshop, Ajou University, Suwon, Korea, October 31, 2014.
- Eulerian polynomials via continued fractions: Part 2, The 2nd KIAS Combinatorics Workshop, KIAS, Seoul, Korea, December 20, 2013.
- Eulerian polynomials via continued fractions, The 1st KIAS Combinatorics Workshop, KIAS, Seoul, Korea, November 8, 2013.
- Simsun permuations and Entringer families, Enumerative Combinatorics mini Workshop 2013, Ladena Condominium, Chuncheon, March 30, 2013.
- (Poster) Minimal transitive factorizations of a permutation of type (p,q), FPSAC 2012, Nagoya, Japan, 2012.
- Trees and parking functions, Math Colloquium, Inha University, Incheon, Korea, March 9, 2011.
- Bijections for Entringer families, 9th Japan-Korea Workshop on Algebra and Combinatorics, Tohoku University, Sendai, Japan, January 25, 2011.
- On
*q*-enumeration of permutations, KAIST Discrete Math Seminar, KAIST, Daejeon, Korea, November 19, 2010. - Certain expansion of Eulerian polynomials via continued fractions, 41st Algebraic Combinatorics Seminar, POSTECH, Pohang, Korea, November 6, 2010.
- On a generalization of Eulerian polynomials via continued fractions, 2010 Global KMS International Conference, POSTECH, Pohang, Korea, October 22, 2010.
- Symmetry and super-symmetry distribution for partitions, SLC 63, Centro Residenziale Universitario di Bertinoro, Bertinoro, Italy, September 27-30, 2009. / slide
- Symmetry and super-symmetry distribution for partitions, 2009 Combinatorics Workshop, KAIST, Daejeon, Korea, August 20-21, 2009.
- (Poster) A further correspondence between (bc,b)-parking functions and
*(bc,b)*-forests, FPSAC 2009, Hagenberg, Austria, July 20-24, 2009. - Counting labelled trees with given indegree sequence, Journées du GDR Informatique Mathématique, Lyon, France, June 15-16, 2009.
- Forests and parking functions, SLC 61, Grande Hotel da Curia, Curia, Portugal, September 21-24, 2008. / slide
- Counting labelled trees with given indegree sequence, KAIST Discrete Math Seminar, KAIST, Daejeon, Korea, August 21, 2008.
- On a decomposition of simple polytopes, Séminaire de Théorie des Nombres et Combinatoire, ICJ, Lyon, France, November 27, 2007.
- On a decomposition of simple polytopes, 2007 Combinatorics Workshop, KAIST, Daejeon, Korea, August 6-8, 2007.
- The bijection between forests and parking functions, 2006 Combinatorics Workshop, Yeoungnam University, Gyeongsan, Korea, August 10, 2006.
- The similarity of forests and parking functions, 2006 Lectures, Center for Combinatorics, Nankai University, Tianjin, China, August 2, 2006.
- Forests and parking functions, 13th Algebraic Combinatorics Seminar, Pusan National University, Pusan, Korea, June 10, 2006.
- Combinatorial objects for
*q*-exponential functions, 2005 Combinatorial Mathematics Conference, Yonsei University, Seoul, Korea, August 8-10, 2005. - Permutation patterns, ordered trees and continued fractions, 2002 KMS Spring Conference, Hoseo University, Cheonan, Korea, April 27, 2002.

## Projects

- June - Nov. 2017 (
**6 months**): Advanced distributed data analysis system and its applications, NIMS, Korea. - March 2017 - Feb. 2022 (
**5 years**): Analysis of statistics for combinatorical objects using Multi-layer Neural Network, NRF, Korea. - Sep. - Dec. 2016 (
**3 months**): Optimization of system for data analytics in industrial mathematics and its applications, NIMS, Korea. - Sep. 2013 - Feb. 2016 (
**2.5 years**): BK21 PLUS Team for Applied Mathematics, NRF, Korea. - May 2012 - April 2015 (
**3 years**): Minimal transitive factorizations of a permutation, NRF, Korea. - Oct. 2008 - Sep. 2010 (
**2 years**): Combinatorics of*q*-series and orthogonal polynomials, CNRS, France - Sep. 2007 - Sep. 2008 (
**1 year**): The refined bijection between the combinatorial objects, KRF, Korea.