# Research

## Research interests

Combinatorics, q-series and special functions

## Publications

Bijections on pattern avoiding inversion sequences and related objects (with JiSun Huh, Sangwook Kim, and, Seunghyun Seo), arXiv:2404.04091, Advances in Applied Mathematics, 161, 102771, 2024.

On Delannoy paths without peaks and valleys (with Seunghyun Seo), arXiv:2203.07770, Discrete Mathematics, 346(7), 2023.

More bijections for Entringer and Arnold families (with Jiang Zeng), arXiv:2006.00507, Electronic Research Archive, 29(2), 2167-2185, 2021. / MR4214065

Refined enumeration of vertices among all rooted ordered d-trees (with Sangwook Kim and Seunghyun Seo), arXiv:1806.06417, Bulletin of the Korean Mathematical Society, 56(4), 899-910, 2019. / MR3992745

The chromatic polynomial for cycle graphs (with Jonghyeon Lee), arXiv:1907.04320, Korean Journal of Mathematics, 27(2), 525-534, 2019. / MR3982944

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

Symmetric unimodal expansions of excedances in colored permutations (with Jiang Zeng), arXiv:1411.6184, European Journal of Combinatorics, 52, part A, 174-196, 2016. / MR3425973

Signed a-polynomials of graphs and Poincaré polynomials of real toric manifolds (with Seunghyun Seo), arXiv:1212.6307, Bulletin of the Korean Mathematical Society, 52(2), 467-481, 2015. / MR3338206

Annular noncrossing permutations and minimal transitive factorizations (with Jang Soo Kim and Seunghyun Seo), arXiv:1201.5703, Journal of Combinatorial Theory, Series A, 124, 251-262, 2014. / MR3176201

A refinement for p-ary labeled trees (with Seunghyun Seo), arXiv:1311.7492, Korean Journal of Mathematics, 21(4), 495-502, 2013.

A refinement for ordered labeled trees (with Seunghyun Seo), arXiv:1207.3291, Korean Journal of Mathematics, 20(2), 225-261, 2012.

The symmetric and unimodal expansion of Eulerian polynomials via continued fractions (with Jiang Zeng), arXiv:1005.4583, European Journal of Combinatorics, 33(2), 111-127, 2012. / MR2854634

On the enumeration of rooted trees with fixed size of maximal decreasing trees (with Seunghyun Seo), arXiv:1106.1290, Discrete Mathematics, 312(2), 419-426, 2012. / MR2852601

Context-dependent transcriptional regulations between signal transduction pathways (with Sohyun Hwang et al), BMC Bioinformatics 2011, 12:19, 2011.

Bijections for Entringer families (with Yoann Gelineau and Jiang Zeng), arXiv:1004.2179, European Journal of Combinatorics, 32(1), 100-115, 2011. / MR2727465

A bijective enumeration of labeled trees with given indegree sequence (with Jiang Zeng), arXiv:0805.0067, Journal of Combinatorial Theory, Series A, 118(1), 115-128, 2011. / MR2737188

The q-tangent and q-secant numbers via continued fractions (with Jiang Zeng), arXiv:0911.4658, European Journal of Combinatorics, 31(7), 1689-1705, 2010. / MR2673011

An involution for symmetry of hook length and part length of partitions (with Jiang Zeng), arXiv:0907.4880, Discrete Mathematics, 310(10-11), 1633-1639, 2010. / MR2601273

A generalized enumeration of labeled trees and reverse prüfer algorithm (with Seunghyun Seo), arXiv:math/0601009, Journal of Combinatorial Theory, Series A, 114(7), 1357-1361, 2007. / MR2353128

Colored prüfer codes for k-edge colored trees (with Manwon Cho et al), Electronic Journal of Combinatorics 11(1), N10, 2004. / MR2097341

## Conference Proceedings

Minimal transitive factorizations of a permutation of type (p,q) (with Jang Soo Kim and Seunghyun Seo), FPSAC 2012, 2012. / PDF

A further correspondence between (bc,b)-parking functions and (bc,b)-forests (with Jiang Zeng), FPSAC 2009, 2009. / DMTCS Proceedings AK, 793-804. / MR2721562

Two involutions on vertices of ordered trees (with Seunghyun Seo), FPSAC 2002, 2002. / PDF

## Preprints

On a decomposition of simple polytopes (with Suyoung Choi), 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

Schöder paths without triple descents and (101,102)-avoiding inversion sequences, 2023 Combinatorics Workshop, Yonsei University, Seoul, Korea, August 16-18, 2023.

(Plenary Talk) Sage Tutorial, Sage Days 116, Sol Beach, Yangyang, Korea, December 27-30, 2022.

(Invited Talk) On Delannoy paths without peaks and valleys, The 24th KIAS Combinatorics Workshop, Shilla Stay Haeundae, Busan, Korea, February 23, 2022.

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

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, France

Sep. 2007 - Sep. 2008 (1 year): The refined bijection between the combinatorial objects, Korea Research Foundation (KRF), Korea.