# Research

## Research interests

Combinatorics,

*q*-series and special functions

## Publications

(with Jiang Zeng) More bijections for Entringer and Arnold families, arXiv:2006.00507, Electronic Research Archive, 2020.

(with Sangwook Kim and Seunghyun Seo) Refined enumeration of vertices among all rooted ordered

*d*-trees, arXiv:1806.06417, Bulletin of the Korean Mathematical Society, 56(4), 899-910, 2019.(with Jonghyeon Lee) The chromatic polynomial for cycle graphs, arXiv:1907.04320, Korean Journal of Mathematics, 27(2), 525-534, 2019.

(with Sen-Peng Eu and Seunghyun Seo) Enumerations of vertices among all rooted ordered trees with levels and degrees, arXiv:1605.00715, Discrete Mathematics, 340(9), 2123-2129, 2017. / MR3665066

(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 of the 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, preprint, 2008.

## Talks

(Invited Talk) Symmetric unimodal expansions of Eulerian polynomials, 2019 KMS Spring Meeting, April 20, 2019, Kangwon National University, Chuncheon, Korea.

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, February 1, 2017

Hot to use JupyterHub for data analysis, Setup of JupyterHub and its application, Korea University, Korea, December 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 Meeting, 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, FranceSep. 2007 - Sep. 2008 (

**1 year**): The refined bijection between the combinatorial objects, Korea Research Foundation (KRF), Korea.