**Dr. Meenakshi Rana**

Associate Professor

**Specialization**

Partition Theory, Enumerative Combinatorics, Number Theory

**Email**

mrana@thapar.edu

Partition Theory, Enumerative Combinatorics, Number Theory

**Website**

https://sites.google.com/thapar.edu/meenakshirana/home

Meenakshi Rana is working as **Associate Professor** with **School of Mathematics**, Thapar Institute of Engineering & Technology, Patiala. She begin her Job at Thapar Institute of Engineering & Technology in 2008. She has published many SCI/SCIE and refereed research articles. Dr Rana has completed two major research projects and is working on third project. She received the ‘Certificate in Academic Practice’ from CAPSL-Trinity College Dublin, Ireland and has been appointed as **Thapar Trinity Academic Fellow**. Apart from her research interest she is highly enthusiastic teacher and enjoys lecturing to her students.

**Education**** **

2010, Ph.D., Mathematics, Panjab University, Chandigarh

2003, M.Sc. (Hons.), Mathematics, Panjab University, Chandigarh

2001, B.Sc. (Hons.), Mathematics, Panjab University, Chandigarh

**Experience**** **

2017--onwards, **Associate Professor**, SOM, Thapar Institute of Engg. & Tech., Patiala, India

2008 -2017, **Assistant Professor**, SOM, Thapar University, Patiala, Punjab, India

2005–2008, **Lecturer**, Chitkara University, Banur, Punjab, India

2004–2005, **Lecturer**, SSIET, Dera Bassi, Punjab, India

**Teaching Interest**

** **Number Theory, Discrete Math, Enumerative Combinatorics, Optimization Techniques, Linear Algebra, Complex Analysis, Graph Theory

**Research Interest**

Partition Theory, Enumerative Combinatorics, q-series, mock theta functions

**Research Project**

**- Project Title:** On Rogers-Ramanujan-Slater type identities and related topics in Partition Theory

**Duration :** From 2019 – (Ongoing)

**Project No.** MTR/2019/000123

**Funding Agency:** ** **Science and Engineering Research Board (SERB), MATRICS

**- Project Title:** on q-series, split n-color partitions and F-partitions

**Duration :** From 2016 –2019 (Completed)

**Project No.** 25(0256)/16/EMR-II

**Funding Agency:** Council for Scientific and Industrial Research (CSIR)

**- Project Title:** On Combinatorics of q-Series, Rogers- Ramanujan type identities and Split n-Color Partitions

**Duration :** From 2016 –2019 (Completed)

**Project No.** 2/48(18)/2016/NBHM(R.P.)/R&D II/14983

**Funding Agency:** National Board for Higher Mathematics (NBHM)

**Abroad Visit (s)**

- University of Illinois, Urbana-Champaign Campus, USA, June 5 - 9, 2019 (Conference)
- Trinity College, Dublin, Ireland Jan 06 - Feb 24, 2018 (Teaching and Learning in Higher Education SPCert-Program)
- Simon Fraser University, Burnaby Campus, Vancouver, Canada, June 15 - June 24, 2015 (Conference)

**Thesis Supervision**

**Ph.D. Thesis**

- Ms. Vasudha (Pursuing)
- Ms. PrabSimrat (Pursuing)
- Ms. Harman Kaur (Pursuing)
- Ms. Shruti Sharma, 2020 “ Combinatorics of Mock Theta Functions and q-series”.
- Ms. Jasdeep Kaur, 2016 “Rogers-Ramanujan identities type identities and Combinatorics”.

**M.Sc. Thesis**

- Watanjeet, 2019, “On Multiplicity of parts in n-colour 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”

**Membership of Professional Institutions, Associations, Societies**

- Life member of Ramanujan Mathematical Society (644)
- Life member of Indian Mathematical Society (R-10- 131)
- Life member of Society for Special function and their Applications (804)
- Life member of Indian Science Congress (L-16404)
- Life member of Punjab Academy of Sciences (L-1406)

**List of Publications**

**Published (SCI/SCIE)**

- S. Sharma and M Rana, ‘A Simple Combinatorial Treatment for the q–Series Interpreted by Agarwal’,
__Utilitas Mathematica__(Accepted) - M Rana, S Sharma, n-Color Compositions and Lattice Paths of Agarwal-Bressoud, Indian Journal of Pure and Applied Mathematics (SCI),
__Indian J Pure Appl Math.,__https://doi.org/10.1007/s13226-021-00120-w, (2021) 52:87–95. (July 2021) - M Rana and N Saikia, Combinatorial interpretations of
*q*-series using*n*-color partitions,__J. Ramanujan Math. Soc.__36, No. 2 (2021) 123–127. (June 2021) - M Rana and S Sharma, “Combinatorics of some fifth and sixth order mock theta functions,
__Electronic Research Archive__, 29(1): 1803-1818 (doi: 10.3934/era.2020092), March 2021. - K. Singla and M Rana, Exact Solutions and Conservation Laws of Multi Kaup-Boussinesq System with Fractional Order,
__Analysis and Mathematical Physics__(2021) 11:30, https://doi.org/10.1007/s13324-020-00467-z (Jan 2021) - A Kumar, M Rana, “On the treatment of partitions as factorization and further analysis
__”, J. Ramanujan Math. Soc.,__35, No. 3 (2020) 263-27 - Komal Singla and M Rana, Symmetries, Explicit Solutions and Conservation Laws for Some Time Space Fractional Nonlinear Systems,
__Reports in Math. Physics__, Vol 86, NO. 2, 2020. - V. Gupta, M Rana and S Sharma, “On Weighted Signed Color Partitions”,
__Proc. Indian Acad. Sci.__(Math. Sci.) (2020) 130:10 Https://Doi.Org/10.1007/S12044-019-0545-1 (0.341) 09, January 2020 - S Sharma, M Rana, On Mock Theta Functions and Weight-Attached Frobenius Partitions,
__Ramanujan Journal__, 50: 289-303, https://doi.org/10.1007/s11139-018-0054-3 - S. Sharma, M. Rana, “Interpreting some fifth and sixth order mock theta functions by attaching weights,”
__J. Ramanujan Math. Soc.__34, No.4 (2019) 401–410, Dec 2019 - 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) March 2019 - 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), JUNE 2019 - 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) - 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) - 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) - 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) - 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, 20 (Impact Factor-0.28) - 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) - M Rana, “Partition Theoretic Interpretations of The A
_{2 }Rogers-Ramanujan Identities”,__ARS -Combinatoria__, 130 (2017), pp 119-129. (Impact Factor-0.268) - 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) - 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) - 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)

**Published (NON-SCI /Refereed Journals)**

- S Sharma and M Rana, ‘Three-way Combinatorial Interpretations of Rogers–Ramanujan Identities’,
__Journal of Indian Math. Soc. (Accepted).__ - V Gupta, M Rana, “Rogers–Ramanujan type identities for (n + t)–color over-partitions’,
__J. of Ramanujan Society of Mathematics and Mathematical Sciences,__Vol. 8, No. 2 (2021), pp. 01-16 - S. Sharma and M. Rana, “Combinatorics Of Third Order Mock Theta Function f(q) and Sixth Order Mock Theta Functions φ(q), ψ(q)”,
__J. of Ramanujan Society of Mathematics and Mathematical Sciences__, Vol. 7, No. 1 (2019), pp. 31-36. - V. Gupta, M Rana, “On Some Combinatorics of Rogers–Ramanujan Type Identities Using Signed Color Partitions” Current Trends in Mathematical Analysis and Its

Interdisciplinary Applications, https://doi.org/10.1007/978-3-030-15242-0_3. - 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) - 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). - 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. - 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.

**Conferences/Workshops**

**Abroad**

- M. Rana,“ Analytics and Combinatorial Number Theory-A legacy of Ramanujan, University of Illinois, June 5-9, 2019, USA
- Trinity College, Dublin, Ireland Jan 06 - Feb 24, 2018 (Teaching and Learning in Higher Education SPCert-Program)
- 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**

- National Center for Mathematics (NCM) Workshop on Modular Forms (2020), IIT Guwahati, Assam, December 14-19, 2020.
- M. Rana, “On Combinatorics of Mock Theta Functions with Attached Weights,” at Amal Jyoti Engineering College, Kanjirapalli, Kottayam, Kerala, India, November 22-24, 2018.
- M. Rana “On Split (n+t)–Color Partitions and 2–color F–partitions,” at Fractional Calculus, Special Functions and their Applications in Computer Science, November 10-12, 2018, Deptt of Mathematics, TDPG College, Jaunpur, UP, India
- 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
- 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.
- M. Rana, “On Combinatorics of RRI”, 18 th Punjab Science Academy Annual Conference, 7-9 February, 2015, DeshBhagat University, Mandi Gobindgarh, Punjab, India.
- M. Rana, “On some extension of Tenth order mock theta functions”, International Conference of Special Functions and Their Applications, 16-18 October, 2014, Thapar Institute of Engineering & Technology, Patiala, India.
- M. Rana, “Three way combinatorial interpretations of some RRI”, International Conference of Special Functions and Their Applications, 13-15 December, 2013, MVNIT, Jaipur, India.
- 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.
- 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.
- 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.
- M. Rana, “On a fifth order mock theta function”, 98th Indian Science Congress, 3-7 Jan, 2011, SRM University, Chennai, India.
- 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.
- M. Rana and A. K. Agarwal, “Partition theoretic interpretation of a fifth order mock theta function” 74th annual conference of IMS, 27-30 Dec, 2008, University of Allahabad, Allahabad, India.
- M. Rana and A. K. Agarwal, “On a Combinatorial identity”, 73th annual conference of IMS, 27-30 Dec, 2007, University of Pune, Pune, India.

**INVITED TALKS**

- “On Combinatorics of Mock Theta Functions with Attached Weights,” at Amal Jyoti Engineering College, Kanjirapalli, Kottayam, Kerala, India, November 22-24, 2018.
- “On Split (n+t)–Color Partitions and 2–color F–partitions,” at Fractional Calculus, Special Functions and their Applications in Computer Science, November 10-12, 2018 and a National Workshop on “Science fare creating awareness, interest, motivation in Science and Mathematics for school students and teachers” , November 10-13, 2018, Deptt of Mathematics, TDPG College, Jaunpur, UP, India
- “q-Series and Split (n+t)-Color Partitions” at International Conference on Special Functions and their Applications, 9-11 September 2016, JamiaMilliaIslamia, New Delhi
- “On Multiple Integrals and its applications in engineering”, October 20, 2015, at Chandigarh Engineering College, Landran, Mohali, Punjab, India.
- “On some extension of Tenth order mock theta functions”, at International Conference of Special Functions and Their Applications, 16-18 October, 2014, Thapar Institute of Engineering & Technology, Patiala, India.
- “Applications of Mathematics in Engineering,” at Rayat and Behra Institute for Women, Khrar, Mohali, February 07, 2014.
- “Three way combinatorial interpretations of some RRI” at International Conference of Special Functions and Their Applications, 13-15 Dec, 2013, MVNIT, Jaipur, India.

**Awards and Honours**

- Awarded $750 Funding by Simon Fraser University, Burnaby during participating in conference “Connections to Discrete Mathematics”
- Awarded Cash Prize for the best paper presentation in Number Theory/Algebra in Indian Mathematical Society Annual Conference (IMS), 2007
- 2
^{nd}Rank in M.Sc. (Hons.) Mathematics, Panjab University, Chandigarh 2003 - 4
^{th}Rank in B.Sc.(Hons.) Mathematics, Panjab University, Chandigarh 2001

**Conferences & Workshops Organized**

- Organized various workshop under Thapar Mathematical Society since 2016.
- Convener: “International Conference of Special Functions and Their Applications”, 16-18 October 2014, Thapar University, Patiala, India
- Convener “Conference on Number Theory, Combinatorics & Special Function (NTCSF-2019)., Thapar Institute of Engineering & Technology, Patiala

**Administrative/Additional Responsibilities**

- President (2015 onwards till date) Thapar Mathematical Society
- Warden-PG hostel (2015-19), Thapar Institute of Engineering & Technology
- Vice President – Kalam (2017 onwards) (Under privileged children society)
- Faculty Advisor (2018 onwards)- Gender Champions Society for students at TIET
- School Profile Coordinator (2010-2013), School of Mathematics.

**Message to Students & Community**

Learn a skill that enable you to learn new skills, built up and work upon for building your learning capabilities.** **Perfection is hard to achieve, but learning allows to improve, even from best of your form.