Scholars@Duke
Lin Jiu

Lin Jiu

Assistant Professor of Mathematics at Duke Kunshan University
DKU Faculty

Selected Publications

A central limit theorem for a card shuffling problem

Journal Article Journal of Combinatorial Theory. Series A · August 1, 2025 Given a positive integer n, consider a permutation of n objects chosen uniformly at random. In this permutation, we collect maximal subsequences consisting of consecutive numbers arranged in ascending order called blocks. Each block is then merged, and aft ... Full text Cite

Information geometry and alpha-parallel prior of the beta-logistic distribution

Journal Article Communications in Statistics - Theory and Methods · January 1, 2025 The hyperbolic secant distribution has several generalizations with applications in, for example, finance. In this study, we explore the dual geometric structure of one such generalization: the beta-logistic distribution. Within this family, two special ca ... Full text Cite

Multi-headed lattices and Green functions

Journal Article Journal of Physics A: Mathematical and Theoretical · November 15, 2024 Lattice geometries and random walks on them are of great interest for their applications in different fields such as physics, chemistry, and computer science. In this work, we focus on multi-headed lattices and study properties of the Green functions for t ... Full text Cite

Hankel determinants and Jacobi continued fractions for q-Euler numbers

Journal Article Comptes Rendus Mathematique · January 1, 2024 The q-analogs of Bernoulli and Euler numbers were introduced by Carlitz in 1948. Similar to recent results on the Hankel determinants for the q-Bernoulli numbers established by Chapoton and Zeng, we perform a parallel analysis for the q-Euler numbers. It i ... Full text Cite

HANKEL DETERMINANTS OF CERTAIN SEQUENCES OF BERNOULLI POLYNOMIALS: A DIRECT PROOF OF AN INVERSE MATRIX ENTRY FROM STATISTICS

Journal Article Contributions to Discrete Mathematics · January 1, 2024 We calculate the Hankel determinants of certain sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries’ natural and deep connection with Bernoul ... Cite

Compatibility of the method of brackets with classical integration rules

Journal Article Open Mathematics · January 1, 2023 The method of brackets is a symbolic approach to the computation of integrals over R n {{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years. This ... Full text Cite

HANKEL DETERMINANTS OF SHIFTED SEQUENCES OF BERNOULLI AND EULER NUMBERS

Journal Article Contributions to Discrete Mathematics · January 1, 2023 Hankel determinants of sequences related to Bernoulli and Euler numbers have been studied before, and numerous identities are known. However, when a sequence is shifted by one unit, the situation often changes significantly. In this paper we use classical ... Full text Cite

Hankel determinants of sequences related to Bernoulli and Euler polynomials

Journal Article International Journal of Number Theory · March 1, 2022 We evaluate the Hankel determinants of various sequences related to Bernoulli and Euler numbers and special values of the corresponding polynomials. Some of these results arise as special cases of Hankel determinants of certain sums and differences of Bern ... Full text Cite

LOOP DECOMPOSITIONS OF RANDOM WALKS AND NONTRIVIAL IDENTITIES OF BERNOULLI AND EULER POLYNOMIALS

Journal Article Integers · January 1, 2022 Let a and b, with a < b, be two level sites of a general random walk. If we partition [a, b] into n arbitrary subintervals with endpoints a < a1 < a2 < · · · < an−1 < b, then the hitting time from a to b can also be decomposed by the hitting times between ... Cite

Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials

Journal Article Journal of Mathematical Analysis and Applications · May 1, 2021 Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials B2k+1(x) and the Euler polynomials E2k+ν(x), for ν=0,1,2. In the process we also determine ... Full text Cite

Calculation and Properties of Zonal Polynomials

Journal Article Mathematics in Computer Science · September 1, 2020 We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer algebra packages, i ... Full text Cite