个人简介
张彪 研究方向为组合数学，主要从事组合数学中单峰型理论和对称函数理论的研究工作。2015年6月博士毕业于南开大学，2018年8月至2019年8月到美国宾夕法尼亚大学访问。在《J.Comb.Theory Ser. A》、《Adv. Appl. Math.》、《SIAM J. Discrete Math.》、《Bull. Lond. Math. Soc.》、《Proc. Amer. Math. Soc.》等期刊发表学术论文三十余篇，主持国家自然科学基金3项、天津市自然科学基金1项。解决了John Stembridge、Francesco Brenti、Christos Athanasiadis、叶永南等人提出的多个猜想； 与合作者定义的多项式被国际同行称为“Haglund-Zhang多项式”，并部分验证了Fields奖得主June Huh提出的拟阵的增广周环Hilbert级数的实根性在均匀拟阵上的情况。 担任天津市数学会理事、天津市工业与应用数学学会理事、中国运筹学会图论组合分会青年理事。
科研项目
1.2025.4-2028.3，排列模式中多统计量联合分布的研究，天津市自然科学基金面上项目 (No. 25JCYBJC00430)，10万，主持
2.2022.1-2025.12, 代数组合学中的若干Schur正性问题, 国家自然科学基金面上项目 (No. 12171362), 50万, 主持
3.2018.1-2020.12, 组合数学中的实根多项式, 国家自然科学基金青年科学基金项目 (No. 11701424), 25万, 主持
4.2017.1-2017.12, 广义欧拉多项式的实根性, 国家自然科学基金数学天元青年基金(No. 11626172), 3万, 主持
5.2019.1-2021.12, 钩长公式及其相关组合问题研究, 国家自然科学基金青年项目 (No.11801447), 25万, 参与
学术论文
1.Matthew H.Y. Xie, Philip B. Zhang, Log-concavity of inverse Kazhdan-Lusztig polynomials of paving matroids, Bulletin of the London Mathematical Society, 58 (1) (2026), e70264.
2.Shuzhen Lv, Philip B. Zhang, Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings, Annals of Combinatorics, (2026), online.
3.Dan Li, Philip B. Zhang, Distributions of mesh patterns of short lengths on king permutations, Discrete Mathematics, 349 (2026), 114681.
4.Shuzhen Lv, Philip B. Zhang, Joint equidistributions of mesh patterns 123 and 132 with minus antipodal shadings, Discrete Applied Mathematics, 379 (2026), 419-433.
5.Tian Han, Sergey Kitaev, Philip B. Zhang, Distribution of maxima and minima statistics on alternating permutations, Springer numbers, and avoidance of flat POPs, Journal of Combinatorial Theory, Series A, 213 (2025), 106034.
6.Harold R.L. Yang, Philip B. Zhang, Stable multivariate Narayana polynomials and labeled plane trees, Advances in Applied Mathematics, 166 (2025), 102867.
7.Alexander Burstein, Tian Han, Sergey Kitaev, Philip B. Zhang, On (shape-)Wilf-equivalence of certain sets of (partially ordered) patterns, Electronic Journal of Combinatorics, 32(1) (2025), #P1.7.
8.Philip B. Zhang, Sergey Kitaev, Descent generating polynomials for (n-3)- and (n-4)-stack-sortable (pattern-avoiding) permutations, Discrete Applied Mathematics, 372 (2025), 1-14.
9.Yujie Du, Philip B. Zhang, On enumeration of pattern-avoiding Fishburn permutations, Discrete Mathematics, 347 (2024), 113952.
10.Siyi Wu, Matthew H.Y. Xie, Philip B. Zhang, The ultra log-concavity of Z-polynomials and gamma-polynomials of uniform matroids, Journal of Difference Equations and Applications, 30 (2024), 1370-1384.
11.Joanna N. Chen, Sergey Kitaev, Philip B. Zhang, Distributions of statistics on separable permutations, Discrete Applied Mathematics, 355 (2024), 169-179.
12.Sergey Kitaev, Philip B. Zhang, Non-overlapping descents and ascents in stack-sortable permutations, Discrete Applied Mathematics, 344 (2024), 112-119.
13.Siyi Wu, Philip B. Zhang, The log-concavity of Kazhdan-Lusztig polynomials of thagomizer matroids, Discrete Mathematics, 346 (2023), 113381.
14.Matthew H.Y. Xie, Philip B. Zhang, The log-concavity of Kazhdan–Lusztig polynomials of uniform matroids, Journal of Systems Science and Complexity, 36 (2023), 117-128.
15.Arthur L.B. Yang, Philip B. Zhang, Descent generating polynomials and the Hermite-Biehler theorem, Journal of Algebraic Combinatorics, 56 (2022), 117-152.
16.Vasu Tewari, Andy Wilson, Philip B. Zhang, Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive, Proceedings of the American Mathematical Society, 150 (2022), 1873-1888.
17.Zhicong Lin, Jun Ma, Philip B. Zhang, Statistics on multipermutations and partial gamma-positivity, Journal of Combinatorial Theory, Series A, 183 (2021), 105488.
18.Alice L.L. Gao, Linyuan Lu, Matthew H.Y. Xie, Arthur L.B. Yang, Philip B. Zhang, The Kazhdan-Lusztig polynomials of uniform matroids, Advances in Applied Mathematics, 122 (2021), 102117.
19.Philip B. Zhang, Interlacing polynomials and the Veronese construction for rational formal power series, Proceedings of the Royal Society of Edinburgh Section A, 150 (1) (2020), 1-16.
20.Sergey Kitaev, Xutong Zhang, Philip B. Zhang, Distributions of several infinite families of mesh patterns, Applied Mathematics and Computation, 372 (2020), 124984.
21.Matthew H.Y. Xie, Philip B. Zhang, Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids, Proceedings of the American Mathematical Society, 147 (2019), 4687-4695.
22.Sergey Kitaev, Philip B. Zhang, Distributions of mesh patterns of short lengths, Advances in Applied Mathematics, 110 (2019), 1-32.
23.James Haglund, Philip B. Zhang, Real-rootedness of variations of Eulerian polynomials, Advances in Applied Mathematics, 109 (2019), 38-54.
24.Philip B. Zhang, On the real-rootedness of the local h-polynomials of edgewise subdivisions of simplexes, Electronic Journal of Combinatorics, 26 (1) (2019), #P1.52.
25.Xutong Zhang, Philip B. Zhang, Multivariate stable Eulerian polynomials on segmented permutations, European Journal of Combinatorics, 78 (2019), 155-162.
26.Alice L.L. Gao, Sergey Kitaev, Wolfgang Steiner, Philip B. Zhang, On a greedy algorithm to construct universal cycles for permutations, International Journal of Foundations of Computer Science, 30 (1) (2019), 61-72.
27.Zhiguang Hu, Philip B. Zhang, Determinants and characteristic polynomials of Lie algebras, Linear Algebra and Its Applications, 563 (2019), 426-439.
28.Philip B. Zhang, The local h-polynomials of cluster subdivisions have only real zeros, Bulletin of the Australian Mathematical Society, 98 (2) (2018), 258-264.
29.Herman Z.Q. Chen, Arthur L.B. Yang, Philip B. Zhang, The Real-rootedness of Generalized Narayana Polynomials related to the Boros-Moll Polynomials, Rocky Mountain Journal of Mathematics, 48 (1) (2018), 107-119.
30.Chunmei Luo, Liancui Zuo, Philip B. Zhang, The Wiener index of Sierpinski-like graphs, Journal of Combinatorial Optimization, 35 (3) (2018), 814-841.
31.Herman Z.Q. Chen, Arthur L.B. Yang, Philip B. Zhang, Kirillov's unimodality conjecture for the rectangular Narayana polynomials, Electronic Journal of Combinatorics, 25 (1) (2018), #P1.17.
32.Alice L.L. Gao, Sergey Kitaev, Philip B. Zhang, On pattern avoiding indecomposable permutations, Integers, 18 (2018), A2.
33.Alice L.L. Gao, Sergey Kitaev, Philip B. Zhang, On 132-representable graphs, Australasian Journal of Combinatorics, 69 (1) (2017), 105-118.
34.Arthur L.B. Yang, Philip B. Zhang, Brenti's open problem on the real-rootedness of q-Eulerian polynomials of type D, SIAM Journal on Discrete Mathematics, 31 (2) (2017), 918-926.
35.Alice L.L. Gao, Sergey Kitaev, Philip B. Zhang, Avoiding vincular patterns on alternating words, Discrete Mathematics, 339 (8) (2016), 2079-2093.
36.Alice L.L. Gao, Sergey Kitaev, Philip B. Zhang, Pattern-avoiding alternating words, Discrete Applied Mathematics, 207 (2016), 56-66.
37.Philip B. Zhang, On the real-rootedness of the descent polynomials of (n-2)-stack sortable permutations, Electronic Journal of Combinatorics, 22 (4) (2015), #P4.12.
38.Arthur L.B. Yang, Philip B. Zhang, The real-rootedness of Eulerian polynomials via the Hermite-Biehler theorem, DMTCS Proceedings, FPSAC 15 (2015), 465-474.
39.Matthew H.Y. Xie, Philip B. Zhang, Derivation of the real-rootedness of coordinate polynomials from the Hermite-Biehler theorem, Acta Mathematica Hungarica, 143 (1) (2014), 185-191.
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