Publications


Journal Articles

1.     A note on partitions into distinct parts and odd parts (with D. Kim), Ramanujan J., 3 (1999), 227-231.

2.     On combinatorics of lecture hall partitions, Ramanujan J., 5 (2001), 247-262.

3.     On the refined lecture hall theorem, Discrete Math., 248 (2002), 293-298.

4.     A combinatorial proof of Andrews' partition functions related to Schur's partition theorem, Proceedings of the Amer. Math. Soc., 130 (2002), 2229-2235.

5.     Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series (with B.C. Berndt and P.R. Bialek), International Mathematics Research Notices, 21 (2002), 1077-1109.

6.    Integrals of Eisenstein series, derivatives of L-functions, and the Dedekind eta-function (with S. Ahlgren, B.C. Berndt, and A. Zaharescu), International Mathematics Research Notices, 32 (2002), 1723-1738.

7.     Ramanujan's contributions to Eisenstein series, especially in his lost notebook (with B.C. Berndt), Number Theoretic Methods - Future Trends, C. Jia and S. Kanemitsu, eds., Kluwer, Dordrecht, pp. 31-53 (2002); abridged version, A survey on Eisenstein series in Ramanujan's lost notebook (with B. C. Berndt), in New Aspects of Analytic Number Theory}, Y. Tanigawa, ed., Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 130--141.

8.    Congruences for the coefficients of quotients of Eisenstein series (with B.C. Berndt), Acta Arithmetica, 104 (2002), 297-308.

9.     On Ramanujan's continued fraction for  (q2; q3)inf/(q;q3)inf (with G.E. Andrews, B.C. Berndt, J. Sohn, and A. Zaharescu), Trans, Amer. Math. Soc., 355 (2003) 2397-2411.

10.   A page on Eisenstein series in Ramanujan's Lost Notebook (with B.C. Berndt), Glasg. Math. J., 45 (2003), 123-129.

11.   On the parity of partition functions (with B.C. Berndt and A. Zaharescu), Internat. J. Math., 14 (2003), 437-459.

12.   Combinatorial proofs of generating function identities for F-partitions, J. Combin. Theory Ser. A, 102 (2003), 217-228.

13.   Theorems on Partitions From a Page in Ramanujan's Lost Notebook (with B.C. Berndt and J. Yi), J. Comput. Appl. Math., 160 (2003), 53-68.

14.   On the generalized Rogers-Ramanujan continued fraction (with B.C. Berndt), Ramanujan J., 7 (2003), 321-331.

15.   Combinatorial proofs of identities in Ramanujan's lost notebook associated with the Rogers-Fine identity and false theta functions (with B. C. Berndt), Ann. Comb., 7 (2003), 409-423.

16.   Combinatorial proofs of Ramanujan's 1\psi_1 summation and the q-Gauss summation, J. Combin. Theory Ser. A, 105 (2004), 63-77.

17.   New theorems on the parity of partition functions (with B.C. Berndt and A. Zaharescu), J. Reine Angew. Math., 566 (2004), 91-109.

18.   On partition functions of Andrews and Stanley, J. Combin. Theory Ser. A, 107 (2004), 313-321. 

19.   q-Gauss summation via Ramanujan and combinatorics (with B. C. Berndt), South East Asian J. Math. Math. Sci, 3 (2004), 15-22.

20.   Partitions with difference conditions and Alder's conjecture, Proc. Natl. Acad. Sci. USA, 101 (2004), 16417-16418.

21.   A new shuffle convolution for multiple zeta values, J. Alg. Combin., 21 (2005), 55-69.

22.   Continued fractions with three limit points (with G. E. Andrews, B. C. Berndt, J. Sohn, and A. Zaharescu), Adv. Math., 192 (2005), 231-258.

23.   A reciprocity theorem for certain q-series found in Ramanujan's lost notebook (with B. C. Berndt, S. H. Chan, and B. P. Yeap), Ramanujan J., 13 (2007), 27-3.

24.   Ramanujan's Forty Identities for the Rogers--Ramanujan Functions (with B. C. Berndt, G. Choi, Y.-S. Choi, H. Hahn, B. P. Yeap, H. Yesilyurt, and J. Yi), Memoirs of the AMS, 188 (2007), 1-97.

25.   Combinatorial proofs of identities in basic hypergeometric series, European J. Combin., 29 (2008), 1365-1375.

26.   Alder's conjecture, J. Reine Angew. Math., 616 (2008), 67-88.

27.   Euler's partition theorem and the combinatorics of l-sequences (with C. D. Savage), J. Combin. Theory Ser. A, 115 (2008), 967-996.

28.   Bijective proofs of a theorem of Fine and related partition identities, Inter. J. Number Theory, 5 (2009), 209-218.

29.   MacMahon's partition identity and the coin exchange problem, J. Combin. Theory Ser. A, 116 (2009), 1228-1231.

30.   A bijective proof of a limiting case of Watson's 8 \phi_7 transformation formula (with M.Rowell), Ramanujan J., 19 (2009), 267-280.

31. A combinatorial proof of the finite Heine transformation formula (with M. Rowell), Integers: Electronic J. Combinatorial Number Theory,  9 (2009), A50, 691-698.

32.   Combinatorics of generalized q-Euler numbers (with T. Huber), J. Combin. Theory Ser. A, 117 (2010), 361-388.

33.   Ramanuajan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions (with B. C. Berndt and B. Kim),  J. Combin. Theory A, 117 (2010) , 957-973.

34. Ramanujan's partial theta series and parity questions, Ramanujan J., 23 (2010), 215-225.

35. Gollnitz-Gordon identities and parity questions in partitions (with S. Kim), European J. Combin., 32 (2011), 288-293.

36. Alternating permutations and the m-th descents (with K. Kursungoz), Discrete Math., 311 (2011), 2610-2622.

37. Euler's partition theorem with upper bounds on multiplicities (with W. Y. C. Chen and A. J. W. Zhu), Electronic J. Combinatorics, 19 (3) (2012),  #P41.

38. Rogers-Ramanujan-Gordon identities, generalized Gollnitz-Gordon idenities, and parity questions (with S. Kim),  J. Combin. Theory A, 120 (2013) , 1038-1056.

39. Generalized higher order spt-functions (with A. Dixit), Ramanujan J., 31 (2013), 191-212.

40. Partitions with difference conditions and Bressoud's conjecture (with S. Kim), J. Combin. Theory A, 126 (2014), 35-69.

41. Truncated Jacobi triple product theorem, J. Combin. Theory A, 130 (2015), 1-14.

42. Partitions associated with the Ramanujan/Watson mock theta functions omega(q), nu(q) and phi(q) (with G. E. Andrews and A. Dixit), Research in Number Theory (2015) 1:19.

43. Legendre theorems for subclasses of overpartitions (with G. E. Andrews),  J. Combin. Theory A, 144 (2016), 16-36.

44.  Arithmetic properties of the Ramanujan/Watson mock theta functions omega(q) and nu(q) (with G. E. Andrews, D. Passary, and J. Sellers), Ramanujan J, 43 (2017), 347-357.  

Conference Proceedings

1.     Overpartitions and generating functions for generalized Frobenius partitions (with S. Corteel and J. Lovejoy), Trends Math. (Birkhauser), 15-24, 2004.


Preprints

1. Overpartitions related to the mock theta function omega(q) (with G. E. Andrews, A. Dixit, and D. Schultz), submitted for publication.

2. Overpartitions and singular overpartitions (with S. Seo),  accepted in Proceedings of the Alladi60 conference (in honor of Krishnaswami Alladis 60th birthday), Mathematics and Statistics Proceedings Series, Springer.

3. Some Hekce-Rogers type identities (with L. Wang), submitted for publication.

4. Enumeration of partitions with prescribed successive rank parity blocks (with S. Seo), submitted for publication.

5. Overpartitions with bounded part differences (with S. Chern), submitted for publication.

6. Combinatorial proofs of two truncated theta series theorems (with C. Ballantine, M. Merca and D. Passary), submitted for pucliation.

7. Some identities associated with mock theta functions omega(q) and nu(q)  (with G. E. Andrews), submitted for publication.



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