Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Interpreting Some Fifth and Sixth Order Mock Theta Functions by Attaching Weights


Affiliations
1 School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, India
2 Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo, India
     

   Subscribe/Renew Journal


A constructive approach is applied to obtain the interpretations of two mock theta functions of order five and four of order six using two-line arrays for (n + t)–color partitions. Interpretations of four mock theta functions are obtained by attaching weights to the partitions generated by their unsigned versions. Further, mappings are established to obtain the interpretations of the same mock theta functions in terms of F–partitions.
User
Subscription Login to verify subscription
Notifications
Font Size

  • A. K. Agarwal, n-color partition theoretic interpretations of some mock theta functions, Electron. J. combin., 11(3) (2004) #N14.

  • A. K. Agarwal and G. E. Andrews, Rogers–Ramanujan identities for partitions with “N copies of N”, J. Combin. Theory Ser. A, 45(1) (1987) 40–49.

  • A. K. Agarwal and G. Narang, Generalized Frobenius partitions and mock theta functions, Ars Combinatoria, 99 (2011) 439–444.

  • A. K. Agarwal and M. Rana, Two new combinatorial interpretations of a fifth order mock theta function, J. Indian Math. Soc., Special Centenary Volume 1907–2007, (2008) 11–24.

  • G. E. Andrews, Generalized Frobenius partitions, volume 301, Amer. Math. Soc. (1984).

  • G. E. Andrews and D. Hickerson, Ramanujan’s “lost” notebook VII: The sixth order mock theta functions, Adv. Math., 89(1) (1991) 60–105.

  • B. C. Berndt and S. H. Chan, Sixth order mock theta functions, Adv. Math., 216(2) (2007) 771–786.

  • E. H. M. Brietzke, J. P. O. Santos and R. Silva, A new approach and generalizations to some results about mock theta functions, Discrete Math., 311(8) (2011) 595–615.

  • S. Ramanujan, The lost notebook and other unpublished papers, Narosa Publishing House, New Delhi (1988).

  • M. Rana and A. K. Agarwal, Frobenius partition theoretic interpretation of a fifth order mock theta function, Canad. J. Pure App. Sci., 3(2) (2009) 859–863.

  • J. P. O. Santos, P. Mondek and A. C. Ribeiro, New two-line arrays representing partitions, Ann. Comb., 15(2) (2011) 341–354.

  • J. K. Sareen and M. Rana, Combinatorics of tenth-order mock theta functions, Proc. Indian Acad. Sci. Math. Sci., 126(4) (2016) 549–556.

  • S. Sharma and M. Rana, Combinatorial interterpretations of mock theta functions by attaching weights, Discrete Math., 341(7) (2018) 1903–1914.

  • S. Sharma and M. Rana, A new approach in interpreting some families of generating functions and mock theta functions, Communicated.

  • S. Sharma and M. Rana, On mock theta functions and weight-attached Frobenius partitions, Ramanujan J. (2018).

  • G. N. Watson, The mock theta functions (2), Proc. London Math. Soc., 2(1) (1937) 274–304.


Abstract Views: 472

PDF Views: 0




  • Interpreting Some Fifth and Sixth Order Mock Theta Functions by Attaching Weights

Abstract Views: 472  |  PDF Views: 0

Authors

S. Sharma
School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, India
M. Rana
Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo, India

Abstract


A constructive approach is applied to obtain the interpretations of two mock theta functions of order five and four of order six using two-line arrays for (n + t)–color partitions. Interpretations of four mock theta functions are obtained by attaching weights to the partitions generated by their unsigned versions. Further, mappings are established to obtain the interpretations of the same mock theta functions in terms of F–partitions.

References