Number Theory and Discrete Mathematics

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.

Multiple Polylogarithms: An Introduction.- A (Conjectural) 1/3-phenomenon for the Number of Rhombus Tilings of a Hexagon which contain a Fixed Rhombus.- The Influence of Carr’s Synopsis on Ramanujan.- A Bailey Lemma from the Quintuple Product.- Little Flowers to G.H. Hardy (07-02-1877-01-12-1947).- Rogers-Ramanujan Type Identities for Burge’s Restricted Partition Pairs Via Restricted Frobenius Partitions.- On q-additive and q-multiplicative Functions.- Antimagic Labeling of Complete m-ary Trees.- Some Recent Advances on Symmetric, Quasi-Symmetric and Quasi-Multiple Designs.- On T-core Partitions and Quadratic Forms.- Observations on Some Algebraic Equations Associated with Ramanujan’s Work.- On Rapidly Convergent Series for Dirichlet L-function Values Via the Modular Relation.- On a Conjecture of Andrews-II.- Integrity of P2× Pn.- A Note on Cordial Labelings of Multiple Shells.- A Report on Additive Complements of the Squares.- Transcendental Infinite Sums and Some Related Questions.- The Lehmer Problem on the Euler Totient: A Pendora’s Box of Unsolvable Problems.- The Problems Solved by Ramanujan in the Journal of the Indian Mathematical Society.- On the gcd and Icm of Matrices Over Dedekind Domains.- The Billiard Ball Motion Problem I: A Markoff Type Chain for the Octahedron in $${{\Re }^{3}}$$.- Hilbert’s Seventeenth Problem and Pfister’s Work on Quadratic Forms.- Certain Representations of Mock-Theta Functions.- Bi-Graceful Graphs.- Wheels, Cages and Cubes.- Relevance of Srinivasa Ramanujan at the Dawn of the New Millennium.- Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil.- On An Additive Question.- n-Colour Partitions.