Identities and Periodic Oscillations of Divide-and-Conquer Recurrences Splitting at Half

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and Periodic Oscillations of Divide-and-Conquer Recurrences Splitting at Half, submitted for publication, October 2022. arXiv pdf (70 pages)

A curious identity in connection with saddle-point method and Stirling's formula

Hsien-Kuei Hwang, A curious identity in connection with saddle-point method and Stirling's formula, submitted for publication, April, 2022. arXiv pdf (Apr. 2022) pdf (revised, Sep. 2023)

Bell numbers in Matsunaga’s and Arima’s Genjikō combinatorics: Modern perspectives and local limit theorems

Xiaoling Dou, Hsien-Kuei Hwang and Chong-Yi Li, Bell numbers in Matsunaga’s and Arima’s Genjikō combinatorics: Modern perspectives and local limit theorems (September, 2021). pdf (1.1M)

Asymptotics and statistics on Fishburn matrices: Dimension distribution and a conjecture of Stoimenow

Hsien-Kuei Hwang, Emma Yu Jin, and Michael Schlosser, Asymptotics and statistics on Fishburn matrices: Dimension distribution and a conjecture of Stoimenow, submitted for publication (2021). pdf

Phase transitions from exp(n^{1/2}) to exp(n^{2/3}) in the asymptotics of banded plane partitions

Wenjie. Fang, Hsien-Kuei Hwang, and Mihyun Kang, Phase transitions from exp(n^{1/2}) to exp(n^{2/3}) in the asymptotics of banded plane partitions, Journal of Combinatorial Theory, Series A, 178 (2021), 105363. pdf.

Sharp bounds on the runtime of the (1+1)-EA via drift analysis and analytic combinatorial tools

Hsien-Kuei Hwang and Carsten Witt (2019), Sharp bounds on the runtime of the (1+1)-EA via drift analysis and analytic combinatorial tools, In: Proc. of Foundations of Genetic Algorithms XV - FOGA 2019, ACM Press, pp. 1-12. doi pdf

Asymptotics and statistics on Fishburn matrices and their generalizations

Hsien-Kuei Hwang and Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, Journal of Combinatorial Theory, Series A, 180 (May 2021), 105413. pdf (54 pages) arXiv

Node profiles of symmetric digital search trees: Concentration properties

Michael Drmota, Michael Fuchs, Hsien-Kuei Hwang, and Ralph Neininger, Node profiles of symmetric digital search trees: Concentration properties, Random Structures and Algorithms, to appear. pdf arxiv

Asymptotic expansions for sub-critical Lagrangean forms

Hsien-Kuei Hwang, Miyun Kang and Guan-Huei Duh, Asymptotic expansions for sub-critical Lagrangean forms, AofA 2018 (Uppsala, June 25-29), LIPICS 110, Paper 29.

Asymptotic distribution of parameters in random maps

Olivier Bodini, Julien Courtiel, Sergey Dovgal and Hsien-Kuei Hwang, Asymptotic distribution of parameters in random maps, AofA 2018 (Uppsala, June 25-29), LIPICS 110, Paper 13.

An asymptotic distribution theory for Eulerian recurrences with applications

Hsien-Kuei Hwang, Hua-Huai Chern and Guan-Huei Duh, An asymptotic distribution theory for Eulerian recurrences with applications, Advances in Applied Mathematics, to appear (2019) pdf (114 pages). arXiv: 1807.01412 Supplementary materials: Eulerian recurrences (P_n(v)=a_n(v)P_{n-1}(v)+b_n(v)(1-v)P_{n-1}'(v)) Degenerate Eulerian recurrences (P_n(v)=a_n(v)P_{n-1}(v)) (refresh the two webpages if the math displays are not properly rendered)

Dependence between path-length and size in random digital trees

Michael Fuchs and Hsien-Kuei Hwang, Dependence between Path-length and Size in Random Digital Trees (a conference version), Journal of Applied Probability, accepted for publication (2017). pdf (934K; 21 pages; 3 figures) arXiv: 1701.02397

Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2))+ f(ceiling(n/2)) + g(n): theory and applications

Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2))+ f(ceiling(n/2)) + g(n): theory and applications, ACM Transactions on Algorithms, Volume 13 Issue 4, Article No. 47, November 2017 (NB: title in the published version changed to "Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications". pdf (1.8M, 49 pages, 46 figures)

Periodic oscillations of divide-and-conquer recurrences with balanced part sizes

Hsien-Kuei Hwang, Periodic oscillations of divide-and-conquer recurrences with balanced part sizes, keynote speech delivered at the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Kraków, Poland, July 4–8, 2016. slides (2.2M)

External profile of symmetric digital search trees (extended abstract)

Michael Drmota, Michael Fuchs, Hsien-Kuei Hwang and Ralph Neininger, External profile of symmetric digital search trees (extended abstract), in Proceedings of ANALCO 2017, pp. 124-130. pdf (179K)

Increasing diamonds

Olivier Bodini, Matthieu Dien, Xavier Fontaine, Antoine Genitrini and Hsien-Kuei Hwang, Increasing diamonds, presented at LATIN 2016 (Latin American Theoretical Informatics Symposium, Ensenada, México, April 11-15 2016) and appeared in Volume 9644 of Lecture Notes in Computer Science, pp. 207-219. pdf (374K; 12 pages)

Dependence between external path-length and size in random tries

Michael Fuchs and Hsien-Kuei Hwang, Dependence between external path-length and size in random tries, accepted for presentation at The 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA'16, Krakow, Poland (July 4-8, 2016). pdf (561K; 12 pages) arXiv:1604.08658 arXiv

Generating random permutations by coin-tossing: classical algorithms, new analysis and modern implementation

Axel Bacher, Olivier Bodini, Hsien-Kuei Hwang, Tsung-Hsi Tsai, Generating random permutations by coin-tossing: classical algorithms, new analysis and modern implementation, ACM Transactions on Algorithms, 13 (2017), Article 24, 43 pages. pdf (835K; 43 pages)

From coin-tossing to rock-paper-scissors and beyond: A log-exp gap theorem for selecting a leader

Michael Fuchs, Hsien-Kuei Hwang, and Yoshiaki Itoh, From coin-tossing to rock-paper-scissors and beyond: A log-exp gap theorem for selecting a leader, Journal of Applied Probability, 54 (2017), 213-235. pdf (264K; 24 pages) arXiv:1507.08145

Dependence and phase changes in random m-ary search trees

Hua-Huai Chern, Michael Fuchs, Hsien-Kuei Hwang, and Ralph Neininger, Dependence and phase changes in random m-ary search trees, Random Structures and Algorithms, 50 (2017), 353-379. pdf (465K; 38 pages) arXiv: 1501.05135