Publications

  1. 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.
  2. 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.
  3. 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. (English translation).
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. S. Chern, On a conjecture of George Beck. II, Math. Student 88 (2019), no. 1-2, 159–164. MR3930713.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. S. Chern and M. G. Dastidar, Some congruences modulo 5 and 25 for overpartitions, to appear in Ramanujan J. 47 (2018), no. 2, 435–445. MR3863649doi: 10.1007/s11139-017-9960-z. (Appendix: An auxiliary result on the double coset Γ0(N)\Γ/Γ, download)
  17. 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. MR3831401doi: 10.1142/S1793042118501154.
  18. S. Chern, S. Fu, and D. Tang, Some inequalities for k-colored partition functions, Ramanujan J. 46 (2018), no. 3, 713–725. MR3826751doi: 10.1007/s11139-017-9989-z.
  19. S. Chern, On a conjecture of George Beck, Int. J. Number Theory 14 (2018), no. 3, 647–651. MR3786639. doi: 10.1142/S1793042118500392.
  20. 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.
  21. 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.
  22. S. Chern and M. G. Dastidar, Congruences and recursions for the cubic partition, Ramanujan J. 44 (2017), no. 3, 559–566. MR3723441doi: 10.1007/s11139-016-9852-7.
  23. 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.
  24. S. Chern, Remarks on the distribution of the primitive roots of a prime, Funct. Approx. Comment. Math. 57 (2017), no. 1, 39–46. MR3704224doi: 10.7169/facm/1612.
  25. S. Chern, An overpartition analogue of partitions with bounded differences between largest and smallest parts, Discrete Math. 340 (2017), no. 12, 2834–2839. MR3698071doi: 10.1016/j.disc.2017.08.003.
  26. S. Chern, A curious identity and its applications to partitions with bounded part differences, New Zealand J. Math. 47 (2017), 23–26. MR3691619.
  27. 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.
  28. S. Chern, New congruences for l-regular overpartitions, Integers 17 (2017), Paper No. A22, 8 pp. MR3657408.
  29. S. Chern, Congruences for 1-shell totally symmetric plane partitions, Integers 17 (2017), Paper No. A21, 7 pp. MR3657407.
  30. 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. MR3573114doi: 10.1016/j.jmaa.2016.10.039.
  31. S. Chern, Integral right triangle and rhombus pairs with a common area and a common perimeter, Forum Geom. 16 (2016), 25–27. MR3474530.
  32. S. Chern, New congruences for 2-color partitions, J. Number Theory 163 (2016), 474–481. MR3459582. doi: 10.1016/j.jnt.2015.12.020.
  33. 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.
  34. 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)
  35. S. Chern and A. Cui, Fibonacci numbers close to a power of 2, Fibonacci Quart. 52 (2014), no. 4, 344–348. MR3276060.
  36. 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 and M. D. Hirschhorn, Some results concerning partitions with designated summands, to appear in Ramanujan J. doi: 10.1007/s11139-019-00198-1.
  2. S. Chern, Note on the square-root partition into distinct parts, to appear in Ramanujan J. doi: 10.1007/s11139-019-00191-8.
  3. S. Chern, An extension of a formula of Jovovic, to appear in Integers. download
  4. S. Chern and M. D. Hirschhorn, Partitions into distinct parts modulo powers of 5, to appear in Ann. Comb.
  5. S. Chern, D. Tang, and E. X. W. Xia, Arithmetic properties of 7-regular partition triples, to appear in Indian J. Pure Appl. Math.
  6. S. Chern, Note on sums involving the Euler function, to appear in Bull. Aust. Math. Soc. doi: 10.1017/S0004972719000066
  7. S. Chern, S. Fu, and D. Tang, Multi-dimensional q-summations and multi-colored partitions, to appear in Ramanujan J. doi: 10.1007/s11139-018-0079-7.
  8. S. Chern, Unlimited parity alternating partitions, to appear in Quaest. Math. doi: 10.2989/16073606.2018.1520320.

Preprints

  1. S. Chern and D. Tang, Representations involving the Rogers–Ramanujan continued fraction and their applications, in preparation.
  2. 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, submitted.
  3. S. Chern, Linked partition ideals, directed graphs and q-multi-summations, submitted. Available at arXiv:1907.06363.
  4. S. Chern, Partitions and the maximal excludant, submitted. Available at arXiv:1905.06304.
  5. S. Chern, Weighted partition rank and crank moments. II. Odd order moments, submitted. download
  6. S. Chern, Asymptotics for the Taylor coefficients of certain infinite products, submitted. Available at arXiv:1902.10839.
  7. S. Chern, Weighted partition rank and crank moments. I. Andrews–Beck type congruences, submitted. download
  8. S. Chern and Z. Li, Kanade–Russell conjectures and linked partition ideals, submitted. Available at arXiv:1809.08655.
  9. S. Chern and C. Wang, Ramanujan-type congruences for 2-color partition triples, submitted. Available at arXiv:1706.05667.

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.