我在李群表示、代数组合和应用数学方面做过研究工作。以下是详细的论文目录,其中论文[A1]来自我在北京大学的硕士学位论文。2019年Springer出版的专著《Permutation Polynomial Interleavers for Turobo Codes》的两处章节标题中称[A1]中的算法为Weng and Dong algorithm.该专著的链接:https://doi.org/10.1007/978-981-13-2625-7
(1) 李群表示
[L11] J. Ding, C.-P. Dong, L. Yang, Dirac series for some real exceptional Lie groups,
Journal of Algebra 559(2020),379-407.
[L10]J. Ding,C.-P. Dong,Unitary representations with Dirac cohomology: a finiteness result for complex Lie groups, Forum Mathematicum 32 (2020), 941-964.
[L9] C.-P. Dong,Unitary representations with Dirac cohomology: finiteness in the real case, International Mathematics Research Notices,https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rny293/5289390
[L8]C.-P. Dong,Unitary representations with non-zero Dirac cohomology for complex E6, Forum Mathematicum 31 (1) (2019), 69-82.
[L7] C.-P. Dong, H. Xue,On the nonvanishing hypothesis for Rankin-Selberg convolutions for GL_n(C)×GL_n(C), Representation Theory 21 (2017), 151-171.
[L6] J. Ding, C.-P. Dong, Spin norm, K-types, and tempered representations, Journal of Lie Theory 26 (2016), 651-658.
[L5] C.-P. Dong, Spin norm, pencils, and the u-small convex hull, Proceedings of the American Mathematical Society 144 (2016), 999-1013.
[L4] C.-P. Dong, On a conjecture of Barbasch and Pandzic, Communications in Algebra 43 (2015), 3382-3388.
[L3] C.-P. Dong, J.-S. Huang,Dirac cohomologyof cohomologically induced modules for reductive Lie groups, American Journal of Mathematics 137 (2015), 37-60.
[L2] C.-P. Dong, On the Dirac cohomology of complex Lie group representations, Transformation Groups 18 (2013), 61-79. Erratum: ibid, 595-597.
[L1] C.-P. Dong, J.-S. Huang,Jacquet modules and Dirac cohomology, Advances in Mathematics 226 (2011), 2911-2934.
(2) 代数组合
[C4] C.-P. Dong,G. Weng,Minuscule representations and Panyushev conjectures, Science China Mathematics 61 (10) (2018), 1759-1744.
[C3] C.-P. Dong, S. Wang,Orbits of antichains in certain root posets, Electronic Journal of Combinatorics 24 (4) (2017), #P4.25.
[C2] C.-P. Dong, Folded bump diagrams for partitions of classical types, Advances in Applied Mathematics 62 (2015), 141-159.
[C1] C.-P. Dong, Ad-nilpotent ideals and the Shi arrangement, Journal of Combinatorial Theory, Series A 120 (2013), 2118-2136.
(3) 应用数学
[A3] D.Gao and C.-P. Dong, Fast diffusion inhibits disease outbreaks, Proceedings of the American Mathematical Society 148 (2020), 1709–1722.
[A2] D.Gao, T.M.Lietman, C.-P. Dong and T.C.Porco, Mass drug administration: the importance of synchrony, Mathematical Medicine and Biology 34 (2017), 241-260.
[A1] G. Weng, C.-P. Dong, A note on permutation polynomials over Z_n, IEEE Transactions on Information Theory 54 (2008),4388-4390.