Introduction
Degree: Ph.D.
Tel:+86-13508970087
Email: liulily@qfnu.edu.cn
Resume
Present position: Professor Qufu normal University
Education:
(Sep. 1999 — Jul. 2003) B.S., School of Mathematics and Statistics, Qufu Normal University.
(Sep. 2003 — Jun. 2009) Ph.D., School of Mathematical Sciences, Dalian University of Technology.
Employment:
(Dec. 2016 — present) Professor, Qufu Normal University
(Aug. 2018 —Jan. 2019) Visiting Scholar, University College London
(Aug. 2015 — Jul. 2016) Visiting Scholar, Dalian University of Technology
(Dec. 2011 — Dec. 2016) Associate Professor, Qufu Normal University
(Jul. 2009 — Dec. 2011) Lecturer, Qufu Normal University
Students:
Xiaoli Li, Ya-Nan Li, Dan Ma (2016)
Mengmeng Dong, Yun Yang (2018)
Guanyu Bao, Wen Zhang (2019)
Xin Jiang, Xuwen Liu (2020)
Bingran Cui, Jie Cao, Chenchen Liu (2021)
Xue Yan (2022)
Zhen Huan, Yuyang Sui (2023)
Yuhui Feng, Mengjie Xu (2024)
Wanming Guo (Ph.D.), Ning Guo, Nan Xiao, Jingrui Zhao (2025)
Longyan Cao, Chengyu Yang (2026)
Research Fields
Distribution of polynomial zeros
Total positivity of matrices
Combinatorial inequalities
Lectures
Advanced Algebra
Abstract Algebra
Basic Number Theory
Combinatorics
Research Projects
Unimodality of P-Eulerian polynomials (2024-2027)
Unimodality of combinatorial polynomials (2019-2022)
Unimodality of the second kind of Stirling numbers (2013-2015)
Real-rootedness and log-convexity of combinatorial sequences (2012)
Publications
(27) MR4912855 - Some interlacing sequences related to the Eulerian and derangement polynomials
Yan, Xue; Liu, Lily Li.
Discrete Math. 348 (2025), no. 11, Paper No. 114598, 16 pp.
(26) MR48488046 - Generalized Eulerian distributions from the wreath product $C_s \wr S_n$
Cui, Bingran; Liu, Lily Li; Yuan, Haiyan.
Indian J. Pure Appl. Math. 56 (2025), no. 1, 125–139.
(25) MR4796064 - Some interlacing properties related to the Eulerian and derangement polynomials
Liu, Lily Li; Yan, Xue.
Adv. in Appl. Math. 162 (2025), Paper No. 102776, 25 pp.
(24) MR4577421 - The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group
Cao, Jie; Liu, Lily Li.
J.Algebraic Combin. 57 (2023), no. 3, 793–810.
(23) MR4575039 - A unified approach to multivariate polynomial sequences with real stability
Huan, Zhen; Liu, Lily Li; Yan, Xue.
Adv. in Appl. Math. 148 (2023), Paper No. 102534, 25 pp.
(22) MR4573751 - Asymptotic normality of the Stirling-Whitney-Riordan triangle Guo, Wan-Ming; Liu, Lily Li.
Filomat 37 (2023), no. 9, 2923–2934.
(21) MR4480737 - Zeros distribution of the reverse strong Turán expressions of polynomial sequences
Liu, Lily Li; Yan, Xue.
Adv. in Appl. Math. 142 (2023), Paper No. 102426, 19 pp.
(20) MR4420915 - Inertia indices and eigenvalue inequalities for Hermitian matrices Zheng, Sai-Nan; Chen, Xi; Liu, Lily Li; Wang, Yi.
Linear Multilinear Algebra 70 (2022), no. 8, 1543–1552.
(19) MR4338711 - The Eulerian distribution on the involutions of the hyperoctahedral group is indeed y-positive
Cao, Jie; Liu, Lily Li.
Graphs Combin. 37 (2021), no. 6, 1943–1951.
(18) MR4228914 - Analytic properties of sextet polynomials of hexagonal systems
Li, Guanru; Liu, Lily Li; Wang, Yi.
J. Math. Chem. 59 (2021), no. 3, 719–734.
(17) MR4208236 - Asymptotic normality of coefficients of some polynomials related to Dowling lattices
Liu, Lily Li; Yang, Yun; Zhang, Wen.
Filomat 34 (2020), no. 9, 2915–2925.
(16) MR4144172 - Cyclic derangement polynomials of the wreath product $C_s \wr S_n$
Liu, Lily Li; Dong, Mengmeng.
Discrete Math. 343 (2020), no. 12, 112109, 10 pp.
(15) MR3900906 - Hankel determinants for generating functions of Catalan-like numbers
Liu, Lily Li; Mu, Lili.
Linear Multilinear Algebra 67 (2019), no. 3, 499–509.
(14) MR3870442 - Summation formulas for Fox-Wright function
Wei, Chuanan; Liu, Lily Li; Gong, Dianxuan.
Discrete Math. Theor. Comput. Sci. 20 (2018), no. 2, Paper No. 9, 14 pp.
(13) MR3790863 - Some properties of the (s,t)-parametric Catalan numbers
Liu, Lily Li; Li, Xiaoli J.
Combin. Math. Combin. Comput. 105 (2018), 289–300.
(12) MR3695905 - Some polynomials related to Dowling lattices and x-Stieltjes moment sequences
Liu, Lily Li; Ma, Dan.
Linear Algebra Appl. 533 (2017), 195–209.
(11) MR3625354 - Taylor expansions for the generating function of Catalan-like numbers
Liu, Lily Li; Li, Xiaoli.
Cogent Math. 3 (2016), Art. ID 1200305, 12 pp.
(10) MR3586466 - Infinite log-monotonicity of the central column sequences of combinatorial triangles
Liu, Lily Li; Li, Ya-Nan; Ma, Dan.
J. Comb. Number Theory 8 (2016), no. 2, 185–191.
(9) MR3558081 - Recurrence relations for linear transformations preserving the strong q-log-convexity
Liu, Lily Li; Li, Ya-Nan.
Electron. J. Combin. 23 (2016), no. 3, Paper 3.44, 11 pp.
(8) MR3510702 - Iterative positive solutions for singular nonlinear fractional differential equation with integral boundary conditions
Liu, Lily Li; Zhang, Xinqiu; Liu, Lishan; Wu, Yonghong.
Adv. Difference Equ. 2016, Paper No. 154, 13 pp.
(7) MR3468057 - Continued fractions and the derangement polynomials of types A and B
Liu, Lily Li.
Ars Combin. 125 (2016), 321–330.
(6) MR3373335 - Strong q-log-convexity of the Eulerian polynomials of Coxeter groups
Liu, Lily Li; Zhu, Bao-Xuan.
Discrete Math. 338 (2015), no. 12, 2332–2340.
(5) MR2988855 - Polynomials with real zeros and compatible sequences
Liu, Lily L.
Electron. J. Combin. 19 (2012), no. 3, Paper 33, 10 pp.
(4) MR2829490 - Linear transformations preserving log-convexity
Liu, Lily L.
Ars Combin. 100 (2011), 473–483.
(3) MR2668115 - Positivity of three-term recurrence sequences
Liu, Lily L.
Electron. J. Combin. 17 (2010), no. 1, Research Paper 57, 10 pp.
(2) MR2356431 - On the log-convexity of combinatorial sequences
Liu, Lily L.; Wang, Yi.
Adv. in Appl. Math. 39 (2007), no. 4, 453–476.
(1) MR2311051 - A unified approach to polynomial sequences with only real zeros Liu, Lily L.; Wang, Yi.
Adv. in Appl. Math. 38 (2007), no. 4, 542–560.
