Publications

Research Interest: Partition Theory, Enumerative Combinatorics, Discrete Mathematics

Research Description: My interest is in the study of $q$--series which plays an important role in combinatorics. The subject has early results due to Euler, Gauss and Cauchy and many important contributions by Ramanujan. The subject is rich and has many applications in topics related to Modular Transformation, Partition Theory, Special functions, Rogers-Ramanujan Type Identities, Congruences, Mock Theta Functions and many other.

Publications:

  1. V. Gupta, M Rana and S Sharma, “On Weighted Signed Color Partitions”, Proc. Indian Acad. Sci. (Math. Sci (2020) 130 :10, http://Doi.Org/10.1007/S12044-019-0545-1 (0.341) (SCI)

  2. S Sharma, M Rana, “A new approach in interpreting some mock theta functions” International journal of Number Theory, Vol. 15, No. 7 (2019) 1369–1383, 2019. (IF: 0.462) (SCI)

  3. M Goyal and M Rana, “Combinatorial Identities For Tenth Order Mock Theta Functions”, Proc. Indian Academy of Sciences, (2019) 129:39 https://doi.org/10.1007/s12044-019-0475-y, (2019)(0.341) (SCI)

  4. M Rana, J. K. Sareen And D. Chawala, “On Generalized q-Series and Split (n+t)-Color Partitions”, Utilitas Mathematica, 108(2018), Page No. 3-19. (IMPACT FACTOR-0.228) (SCI)

  5. S Sharma, M Rana, On Mock Theta Functions and Weight-Attached Frobenius Partitions, Ramanujan Journal, https://doi.org/10.1007/s11139-018-0054-3 (2018) (SCI)

  6. M Goyal and M Rana, “On Central Tendencies of the Parts in Certain Restricted Partitions”, Mathematical Reports, Vol. 20(70)3, Page No. 291-300, (2018) (IMPACT Factor-0.341) (SCI)

  7. S Sharma, M Rana, “Combinatorial interpretations of mock theta functions by attaching weights”, Discrete Mathematics Vol. 341 (2018) PP 1903–1914. (IMPACT FACTOR-0.728) (SCI)

  8. M Rana and M Goyal, “On Combinatorics of Modified Lattice Paths and Generalized q-series”, Contributions to Discrete Math., Vol. 13, No. 1, pp 136-149, ISSN 1715-0868, (2018). (IMPACT FACTOR-0.419) (SCI)

  9. M Rana and J K Sareen, “Split (n+t)-Color Partitions and 2-Color F-Partitions”, Contributions to Discrete Math., Vol. 12, No. 2, pp 115-145, ISSN 1715-0868, 2017. (IMPACT FACTOR-0.28) (SCI)

  10. J K Sareen and M Rana, “Four-way combinatorial interpretations of some Rogers-Ramanujan type identities”, ARS-Combinatoria, 133(2017), pp 17-35. (IMPACT FACTOR-0.268) (SCI)

  11. M RANA, “PARTITION THEORETIC INTERPRETATIONS OF THE A2 ROGERS-RAMANUJAN IDENTITIES”, ARS -Combinatoria, 130 (2017), PP 119-129. (IMPACT FACTOR-0.268) (SCI)

  12. J K Sareen and M Rana, “Combinatorics of Tenth Order Mock Theta functions”, PROC. INDIAN ACAD. SCI. (MATH. SCI), Vol. 126, No. 4, November 2016, pp. 549-556. (IMPACT FACTOR-0.371) (SCI)

  13. A K AGARWAL AND M RANA, New combinatorial versions of Gollnitz- Gordon identities, UTILITAS MATHEMATICA, VOL. 79 (2009), PP. 145-155. (IMPACT FACTOR-0.28) (SCI)

  14. M RANA AND A K AGARWAL, On an extension of a combinatorial identities, PROC. INDIAN ACAD. SCI. (MATH. SCI), VOL. 119, NO. 1, (2009), PP. 1-7. (IMPACT FACTOR-0.371) (SCI)

  15. M Rana and J K Sareen, “On Combinatorial Extensions of Some Mock Theta Functions Using Signed Partitions”, Advances in Theoretical and Applied Mathematics, Vol. 10, No.1, pp 15-25 (2015)

  16. A K AGARWAL AND M RANA, “Combinatorial interpretation of a generalized basic series”, Analytic Number Theory, approximation Theory, and special functions, DOI 10.1007/978-1-4939-0258-3_7 HMS-Volume, Springer, 215-225 (2013).

  17. A K Agarwal and M Rana, Two new combinatorial interpretations of a fifth order mock theta function, Journal of The Indian Mathematical Society, Special Centenary Volume (1907-2007), (2009), pp 11-24.

  18. M Rana and A K Agarwal, Frobenius partition theoretic interpretation of a fifth order mock theta function, Canadian Journal of Pure & Applied Sciences, Vol. 3, No.2, (2009), pp. 859-863.

Post Doc Research Fellow

  • Dr. Komal Singla (2017-19)

Ph.D. Research Scholars

Ongoing

  • Ms. Vasudha

  • Ms. Prabsimrat Kaur

  • Ms. Harman Kaur

Completed

  • Ms. Shruti Sharma (Thesis Submitted)

  • Ms. Jasdeep Kaur (2012-2016) "Rogers Ramanujan type Identities and Combinatorics"

M.Sc. Research Scholars

  • Watanjeet Singh 2019, "On multiplicity of parts in n-color compositions"

  • Amrinder Kaur 2017, “On plane partitions and colored partitions”

  • Priyanka, 2016, ‘‘ A survey on colored partition and q-series”

  • Diksha Chawala, 2015, “ Rogers-Ramanujan Identities and split (n+t) color Partition”

  • Nisha, 2015, “On Study of Lattice Paths”

  • Shelja Dutta, 2014, “On n-colour Compositions”

  • Avneet Kaur, 2013, “A Study of ordinary, colored and signed Gollnitz-Gordon identities”

  • Rajni Mittal, 2012, “A Study of Gollnitz-Gordon identities”

  • Richa Bansal, 2011, “A Study of Guassian polynomial”

  • Rajni Bansal, 2011, “Combinatorial interpretations of Rogers-Ramanujan identities and their analogues”

  • Inderpal Singh, 2010, “A Study of Coloured partitions”

Other Undergraduate Scholars

  • Mr. Abhimanyu Kumar (2018-2020)

CONFERENCES/VISIT

Abroad

  • M. Rana, “ Analytics and Combinatorial Number Theory-A legacy of Ramanujan, University of Illinois, June 5-9, 2019, USA

  • M. Rana, Train the Trainer Program, Teaching and Learning in Higher Education, Trinity College Dublin, Dublin. Jan-Febrauary 2018

  • M. Rana, “Split (n+t)-Color Partitions and 2-Color F-Partitions”, Connections in Discrete Mathematics, 15-19 June, 2015, Simon Fraser University, Burnaby, Canada.

India

  1. M. Rana, “q-Series and Split (n+t)-Color Partitions”, International Conference on Special Functions and their Applications, 9-11 September 2016, Jamia Millia Islamia, New Delhi

  2. M. Rana, “On Split (n+t)-Color Partitions, 2-Color F-Partitions and Mock Theta Functions”, South Asian Mathematics Research Scholars Meet , 8-9 May, 2015, South Asian University, New Delhi.

  3. M. Rana, “On Combinatorics of RRI”, 18th Punjab Science Academy Annual Conference, 7-9 February, 2015, Desh Bhagat University, Mandi Gobingarh, Punjab, India.

  4. M. Rana, “On some extension of Tenth order mock theta functions”, International Conference of Special Functions and Their Applications, 16-18 October, 2014, Thapar University, Patiala, India.

  5. M. Rana, “Three way combinatorial interpretations of some RRI”, International Conference of Special Functions and Their Applications, 13-15 December, 2013, MVNIT, Jaipur, India.

  6. M. Rana and H.Kaur, “Combinatorial interpretations of some tenth order mock theta functions”, National Conference on Advances in Mathematics & its Applications in Mathematics & its Applications, 25-27 June, 2013, NIT, Hamirpur, India.

  7. M. Rana, “Partition theoretic interpretations of Some double series q- identities”, International Conference of Special Functions and Their Applications, 27-29 June, 2012, SVNIT, Surat, India.

  8. M. Rana, “Partition theoretic interpretations of RR type identities”, Twenty first International conference of forum for Interdisciplinary Mathematics, 15-17 Dec, 2012, P.U., Chandigarh, India.

  9. M. Rana, “On a fifth order mock theta function”, 98th Indian Science Congress, 3-7 Jan, 2011, SRM University, Chennai, India.

  10. M. Rana and A.K.Agarwal, “New combinatorial versions of Gollnitz-Gordon identities” 11th Punjab Science congress, 7-9 Feb, 2008, T. U., Patiala, India.

  11. M. Rana and A.K.Agarwal, “Partition theoretic interpretation of a fifth order mock theta function” 74rd annual conference of IMS, 27-30 Dec, 2008, University of Allahabad, Allahabad, India.

  12. M. Rana and A.K.Agarwal, “On a Combinatorial identity”, 73rd annual conference of IMS, 27-30 Dec, 2007, University of Pune, Pune, India.

INVITED TALKS

  1. “q-Series and Split (n+t)-Color Partitions” International Conference on Special Functions and their Applications, 9-11 September 2016, Jamia Millia Islamia, New Delhi

  2. “On Multiple Integrals and its applications in engineering, October 20, 2015, Chandigarh Engineering College, Landran, Mohali, Punjab, India.

  3. “On some extension of Tenth order mock theta functions”, International Conference of Special Functions and Their Applications, 16-18 October, 2014, Thapar University, Patiala, India.

  4. “Applications of Mathematics in Engineering, Rayat and Behra Institute for Women, Khrar, Mohali, February 07, 2014.

  5. “Three way combinatorial interpretations of some RRI” International Conference of Special Functions and Their Applications, 13-15 Dec, 2013, MVNIT, Jaipur, India.

WORKSHOP

Workshop on MATLAB Fundamentals by MathWorks Training Services, 17-19 March, 2016

Events Organized

ICSFA-2014


NTCSF-2019