Publications

  1. S. Chern, 1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5, Ramanujan J. 55 (2021), no. 2, 713–731. MR4260169. doi: 10.1007/s11139-020-00306-6.
  2. S. Chern and D. Tang, The Rogers–Ramanujan continued fraction and related eta-quotient representations, Bull. Aust. Math. Soc. 103 (2021), no. 2, 248–259. MR4229493. doi: 10.1017/S0004972720000933.
  3. S. Chern, Note on the square-root partition into distinct parts, Ramanujan J. 54 (2021), no. 2, 449–461. MR4204766. doi: 10.1007/s11139-019-00191-8.
  4. S. Chern and M. D. Hirschhorn, Some results concerning partitions with designated summands, Ramanujan J. 54 (2021), no. 2, 385–395. MR4204762. doi: 10.1007/s11139-019-00198-1.
  5. G. E. Andrews and S. Chern, A proof of Lin’s conjecture on inversion sequences avoiding patterns of relation triples, J. Combin. Theory Ser. A 179 (2021), 105388, 20 pp. MR4190575. doi: 10.1016/j.jcta.2020.105388.
  6. S. Chern and D. Tang, Vanishing coefficients in quotients of theta functions of modulus five, Bull. Aust. Math. Soc. 102 (2020), no. 3, 387–398. MR4176682. doi: 10.1017/S0004972720000271.
  7. C. Wang and S. Chern, Some basic hypergeometric transformations and Rogers–Ramanujan type identities, Integral Transforms Spec. Funct. 31 (2020), no. 11, 873–890. MR4161758. doi: 10.1080/10652469.2020.1760267.
  8. S. Chern, Linked partition ideals, directed graphs and q-multi-summations, Electron. J. Combin. 27 (2020), no. 3, Paper No. 3.33, 29 pp. MR4245146.  doi: 10.37236/9446.
  9. M. Bian, S. Chern, D. D. M. Sang, and E. X. W. Xia, Ramanujan’s theta function identities and the relations between sums of squares and sums of triangular numbers, Int. J. Number Theory 16 (2020), no. 6, 1275–1294. MR4120476. doi: 10.1142/S1793042120500669.
  10. S. Chern, D. Tang, and E. X. W. Xia, Arithmetic properties of 7-regular partition triples, Indian J. Pure Appl. Math. 51 (2020), no. 2, 717–733. MR4115620. doi: 10.1007/s13226-020-0426-4.
  11. S. Chern and Z. Li, Linked partition ideals and Kanade–Russell conjectures, Discrete Math. 343 (2020), no. 7, 111876, 24 pp. MR4072958. doi: 10.1016/j.disc.2020.111876.
  12. S. Chern, S. Fu, and D. Tang, Multi-dimensional q-summations and multi-colored partitions, Ramanujan J. 51 (2020), no. 2, 297–306. MR4056853. doi: 10.1007/s11139-018-0079-7.
  13. S. Chern, Unlimited parity alternating partitions, Quaest. Math. 42 (2019), no. 9, 1345–1352. MR4040863.  doi: 10.2989/16073606.2018.1520320.
  14. S. Chern and M. D. Hirschhorn, Partitions into distinct parts modulo powers of 5, Ann. Comb. 23 (2019), no. 3-4, 659–682. MR4039555.  doi: 10.1007/s00026-019-00439-6.
  15. S. Chern, An extension of a formula of Jovovic, Integers 19 (2019), Paper No. A47, 7 pp. MR4017188.
  16. S. Chern, Note on sums involving the Euler function, Bull. Aust. Math. Soc. 100 (2019), no. 2, 194–200. MR4001535. doi: 10.1017/S0004972719000066. (Erratum)
  17. S. Chern, On a problem of George Andrews concerning partitions with even parts below odd parts, Afr. Mat. 30 (2019), no. 5-6, 691–695. MR3993626. doi: 10.1007/s13370-019-00676-1.
  18. S. Chern, D. Tang, and L. Wang, Some inequalities for Garvan’s bicrank function of 2-colored partitions, Acta Arith. 190 (2019), no. 2, 171–191. MR3984264. doi: 10.4064/aa180507-7-11.
  19. T. Cai, H. Zhong, and S. Chern, A congruence involving the quotients of Euler and its applications. III (in Chinese), Acta Math. Sin. (Chin. Ser.) 62 (2019), no. 4, 529–540. MR3970566. (English translation).
  20. C. Wang and S. Chern, Some q-transformation formulas and Hecke type identities, Int. J. Number Theory 15 (2019), no. 7, 1349–1367. MR3982813. doi: 10.1142/S1793042119500751.
  21. S. Chern, Combinatorial proof of an identity of Andrews and Yee, Ramanujan J. 49 (2019), no. 3, 505–513. MR3979687. doi: 10.1007/s11139-018-0012-0.
  22. S. Chern, A further look at the truncated pentagonal number theorem, Acta Arith. 189 (2019), no. 4, 397–403. MR3962837. doi: 10.4064/aa180718-6-11.
  23. S. Chern and S. Qiu, Partitions, geometric progressions and a Putnam problem, Math. Gaz. 103 (2019), no. 557, 337–343. MR3961649. doi: 10.1017/mag.2019.71.
  24. S. Chern, On a conjecture of George Beck. II, Math. Student 88 (2019), no. 1-2, 159–164. MR3930713.
  25. S. Chern and L.-J. Hao, Congruences for two restricted overpartitions, Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 3, Art. 31, 16 pp. MR3938513. doi: 10.1007/s12044-019-0474-z.
  26. W. Lin, S. Li, S. Chern, and J. E. Zhang, Pricing VIX derivatives with free stochastic volatility model, Rev. Deriv. Res. 22 (2019), no. 1, 41–75. doi: 10.1007/s11147-018-9145-y.
  27. S. Chern, Asymptotics for the Fourier coefficients of eta-quotients, J. Number Theory 199 (2019), 168–191. MR3926193. doi: 10.1016/j.jnt.2018.11.008.
  28. S. Chern and L.-J. Hao, Congruences for partition functions related to mock theta functions, Ramanujan J. 48 (2019), no. 2, 369–384. MR3911794. doi: 10.1007/s11139-017-9979-1.
  29. S. Chern and D. Tang, On certain weighted 7-colored partitions, Ramanujan J. 48 (2019), no. 2, 305–322. MR3911790. doi: 10.1007/s11139-017-9978-2.
  30. S. Chern, On the power mean of a sum analogous to the Kloosterman sum, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 62(110) (2019), no. 1, 77–92. MR3930926.
  31. S. Chern, Note on the truncated generalizations of Gauss’s square exponent theorem, Rocky Mountain J. Math. 48 (2018), no. 7, 2211–2222. MR3892131. doi: 10.1216/RMJ-2018-48-7-2211.
  32. S. Chern and M. G. Dastidar, Some congruences modulo 5 and 25 for overpartitions, Ramanujan J. 47 (2018), no. 2, 435–445. MR3863649. doi: 10.1007/s11139-017-9960-z. (Appendix: An auxiliary result on the double coset Γ0(N)\Γ/Γ∞, download)
  33. P. Adansie, S. Chern, and E. X. W. Xia, New infinite families of congruences for the number of tagged parts over partitions with designated summands, Int. J. Number Theory 14 (2018), no. 7, 1935–1942. MR3831401. doi: 10.1142/S1793042118501154.
  34. S. Chern, S. Fu, and D. Tang, Some inequalities for k-colored partition functions, Ramanujan J. 46 (2018), no. 3, 713–725. MR3826751. doi: 10.1007/s11139-017-9989-z.
  35. S. Chern, On a conjecture of George Beck, Int. J. Number Theory 14 (2018), no. 3, 647–651. MR3786639. doi: 10.1142/S1793042118500392.
  36. S. Chern, T. Cai, and H. Zhong, On the cardinality and sum of reciprocals of primitive sequences, Adv. Math. (China) 47 (2018), no. 1, 150–154. MR3816359. doi: 10.11845/sxjz.2016046b.
  37. S. Chern and A. J. Yee, Overpartitions with bounded part differences, European J. Combin. 70 (2018), 317–324. MR3779621. doi: 10.1016/j.ejc.2018.01.003.
  38. S. Chern and M. G. Dastidar, Congruences and recursions for the cubic partition, Ramanujan J. 44 (2017), no. 3, 559–566. MR3723441. doi: 10.1007/s11139-016-9852-7.
  39. S. Chern, Arithmetic properties for cubic partition pairs modulo powers of 3, Acta Math. Sin. (Engl. Ser.) 33 (2017), no.11, 1504–1512. MR3712396. doi: 10.1007/s10114-017-7052-z.
  40. S. Chern, Remarks on the distribution of the primitive roots of a prime, Funct. Approx. Comment. Math. 57 (2017), no. 1, 39–46. MR3704224. doi: 10.7169/facm/1612.
  41. S. Chern, An overpartition analogue of partitions with bounded differences between largest and smallest parts, Discrete Math. 340 (2017), no. 12, 2834–2839. MR3698071. doi: 10.1016/j.disc.2017.08.003.
  42. S. Chern, A curious identity and its applications to partitions with bounded part differences, New Zealand J. Math. 47 (2017), 23–26. MR3691619.
  43. S. Chern, Distribution of reducible polynomials with a given coefficient set, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 60(108) (2017), no. 2, 141–146. MR3676583.
  44. S. Chern, New congruences for l-regular overpartitions, Integers 17 (2017), Paper No. A22, 8 pp. MR3657408.
  45. S. Chern, Congruences for 1-shell totally symmetric plane partitions, Integers 17 (2017), Paper No. A21, 7 pp. MR3657407.
  46. W. Lin, S. Li, X. Luo, and S. Chern, Consistent pricing of VIX and equity derivatives with the 4/2 stochastic volatility plus jumps model, J. Math. Anal. Appl. 447 (2017), no. 2, 778–797. MR3573114. doi: 10.1016/j.jmaa.2016.10.039.
  47. S. Chern, Integral right triangle and rhombus pairs with a common area and a common perimeter, Forum Geom. 16 (2016), 25–27. MR3474530.
  48. S. Chern, New congruences for 2-color partitions, J. Number Theory 163 (2016), 474–481. MR3459582. doi: 10.1016/j.jnt.2015.12.020.
  49. S. Chern, Formulas for partition k-tuples with t-cores, J. Math. Anal. Appl. 437 (2016), no. 2, 841–852. MR3456201. doi: 10.1016/j.jmaa.2016.01.040.
  50. S. Chern, A note on balancing binomial coefficients, Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 8, 110–111. MR3403941. doi: 10.3792/pjaa.91.110. (Appendix: Programs for “A note on balancing binomial coefficients”, download)
  51. S. Chern and A. Cui, Fibonacci numbers close to a power of 2, Fibonacci Quart. 52 (2014), no. 4, 344–348. MR3276060.
  52. S. Chern, Fermat numbers in multinomial coefficients, J. Integer Seq. 17 (2014), no. 3, Article 14.3.2, 5 pp. MR3168684.

Accepted Manuscripts

  1. S. Chern, Partitions and the maximal excludant, to appear in Electron. J. Combin. download
  2. S. Chern, Further results on biases in integer partitions, to appear in Bull. Korean Math. Soc. download
  3. S. Chern, Weighted partition rank and crank moments. III. A list of Andrews–Beck type congruences modulo 5, 7, 11 and 13, to appear in Int. J. Number Theory. download
  4. S. Chern, Note on partitions with even parts below odd parts, to appear in Math. Notes. download
  5. S. Chern and D. Tang, Vanishing coefficients and identities concerning Ramanujan’s parameters, to appear in Ramanujan J. doi: 10.1007/s11139-021-00385-z.
  6. S. Chern, Weighted partition rank and crank moments. II. Odd-order moments, to appear in Ramanujan J. doi: 10.1007/s11139-020-00365-9.
  7. S. Chern, Weighted partition rank and crank moments. I. Andrews–Beck type congruences, to appear in Proceedings of the Conference in Honor of Bruce Berndt. download
  8. S. Chern and D. Tang, 5-Dissections and sign patterns of Ramanujan’s parameter and its companion, to appear in Czechoslovak Math. J. doi: 10.21136/CMJ.2021.0218-20.
  9. S. Chern, Asymptotics for the Taylor coefficients of certain infinite products, to appear in Ramanujan J. doi: 10.1007/s11139-020-00273-y.

Preprints

  1. G. E. Andrews, S. Chern, and Z. Li, On the k-measure of partitions and distinct partitions, submitted. Available at arXiv:2105.01758.
  2. S. Chern, A different look at Euclidean billiard partitions, submitted. Available at arXiv:2012.14485.
  3. S. Chern, On 0012-avoiding inversion sequences and a Conjecture of Lin and Ma, submitted. Available at arXiv:2006.04318.
  4. N. Chen, S. Chern, Y. Fan, and E. X. W. Xia, Some generating functions and inequalities for the Andrews–Stanley partition functions, submitted.
  5. S. Chern, Nonmodular infinite products and a Conjecture of Seo and Yee, submitted. Available at arXiv:1912.10341.

Other Publications

  1. X. Chen, Liu shao qing (in Chinese), Chinese Poetry Monthly 14 (2010), 23.
  2. X. Chen, Selected poems of Xiao-Hang (in Chinese), Chien Kun Poetry Quart. Classic Poetry Ser. 53 (2010), 21–22.