Number Theory and Discrete Mathematics

1. Front Matter

   Pages i-xvi

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2. Multiple Polylogarithms: An Introduction

   • M. Waldschmidt

   Pages 1-12

3. A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which Contain a Fixed Rhombus

   • C. Krattenthalert

   Pages 13-30

4. The Influence of Carr’s Synopsis on Ramanujan

   • Bruce C. Berndt

   Pages 31-35

5. A Bailey Lemma from the Quintuple Product

   • George E. Andrews

   Pages 37-46

6. Little Flowers to G.H. Hardy(07-02-1877–01-12-1947)

   • K. Ramachandra

   Pages 47-51

7. Rogers-Ramanujan Type Identities for Burge’s Restricted Partition Pairs Via Restricted Frobenius Partitions

   • A. K. Agarwal, Padmavathamma

   Pages 53-60

8. On q-additive and q-multiplicative Functions

   • I. Kátai

   Pages 61-76

9. Antimagic Labeling of Complete m-ary Trees

   • P. D. Chawathe, Vijaya Krishna

   Pages 77-80

10. Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs

    • Sharad Sane

    Pages 81-88

11. On T-core Partitions and Quadratic Forms

    • Neville Robbins

    Pages 89-100

12. Observations on Some Algebraic Equations Associated with Ramanujan’s Work

    • Michele Elia

    Pages 101-111

13. On Rapidly Convergent Series for Dirichlet L-function Values Via the Modular Relation

    • S. Kanemitsu, Y. Tanigawa, M. Yoshimoto

    Pages 113-133

14. On a Conjecture of Andrews-II

    • Padmavathamma, M. Ruby Salestina

    Pages 135-147

15. Integrity of P ₂ x P _n

    • P. D. Chawathe, S. A. Shende

    Pages 149-155

16. A Note on Cordial Labelings of Multiple Shells

    • Mahesh Andar, Samina Boxwala, N. B. Limaye

    Pages 157-160

17. A Report on Additive Complements of the Squares

    • D. S. Ramana

    Pages 161-167

18. Transcendental Infinite Sums and Some Related Questions

    • Sukumar Das Adhikari

    Pages 169-178

19. The Lehmer Problem on the Euler Totient: A Pendora’s Box of Unsolvable Problems

    • M. V. Subbarao

    Pages 179-187

20. The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society

    • Bruce C. Berndt

    Pages 189-200

To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana­ Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.

• algebraic geometry
• discrete mathematics
• number theory
• combinatorics

• Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

  A. K. Agarwal

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