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1 2 Sri Ramajayam INTERNATIONAL CONFERENCE on NUMBER THEORY & COMBINATORICS" DECEMBER 2006 INTERNATIONAL CONFERENCE ON Organised by SRINIVASA RAMANUJAN CENTRE SHANMUGHA ARTS, SCIENCE, TECHNOLOGY & RESEARCH ACADEMY (SASTRA) DEEMED UNIVERSITY KUMBAKONAM TAMILNADU, INDIA

2 BACKGROUND Number Theory, which originated as that defining the structure and properties of ordering integers, has expanded into the study of similar properties of other rings. The methods employed in the study are varied such as Algebraic (like group theory, ring theory and field theory), Geometric (like Algebraic Geometry of curves and higher dimensional varieties) and Combinatorial (such as Graph Theory, Generating functions, etc.). Combinatorics is the science that studies the number of different combinations which are groupings of numbers. Combinatorics, thus associated with a finite set that includes some additional structure (like a projective geometry, a graph or a block design), tries to relate a known set or tries to show how a certain structure can or cannot be imposed on a given set. According to Prof. Laszlo Lovasz, a very distinguished Hungarian Mathematician, Combinatorics has now burgeoned into one of the fastest growing branches of mathematics - undoubtedly so if we consider the number of publications in this field, its applications in other branches of mathematics and in other sciences, and also, the interest of scientists, economists and engineers in combinatorial structures. The mathematical world has been attracted by the successes of algebra and analysis and only in recent years has it become clear, due largely to problems arising from economics, statistics, electrical engineering and other applied sciences, that Combinatorics, the study of finite sets and finite structures, has its own problems and principles. These are independent of those in algebra and analysis but match them in difficulty, practical and theoretical interest and beauty." In addition, the progress of theoretical computer science has resulted in a great deal of fusion between Combinatorics and Number Theory. Srinivasa Ramanujan, the Mathematical th Genius who lived in the 20 century, has contributed not only to number theory, but also to algebra and analysis. Ramanujan laid the foundations for research in Partitions, Continued Fractions and Combinatorial Analysis. His work on mock theta functions and modular equations, during the last years of his life, has opened up new vistas for research. Many modern mathematicians have found the Notebooks of Ramanujan as inspiring sources for their researches.

3 OBJECTIVES The objective of the conference is to provide a platform for exchange of ideas between experts and researchers in the field of Number Theory, Combinatorics and Ramanujan Mathematics. This conference, it is hoped, will not only provide more insights into these areas but also help forge new areas of interdisciplinary research. SESSIONS th 19 December, am To am - Inauguration am To am - Tea Break am To pm - Session I pm To pm - Lunch pm To pm - Session II pm To pm - Tea Break pm To pm - Session III (Paper Presentation) th 20 December, am To am - Session IV am To am - Tea Break am To pm - Session V pm To pm - Lunch pm To pm - Session VI pm To pm - Tea Break pm To pm - Visit to Ramanujan's House and places of worship in and around Kumbakonam. st 21 December, am To am - Session VII am To am - Tea Break am To pm - Session VIII pm To pm - Lunch pm To pm - Session IX (Paper Presentation) pm To pm - Tea nd 22 December, am To am - Commemorative Lecture am To am - Tea Break am To noon - Session X noon To pm - Lunch pm - Valedictory SRINIVASA RAMANUJAN COMMEMORATIVE LECTURE th A Commemorative Lecture to mark the 120 Birth Anniversary of the Mathematical wizard, Srinivasa Ramanujan, will be delivered by the SASTRA- Ramanujan Award Winner on December 22, 2006.

4 CALL FOR PAPERS Distinguished researchers, both from India and abroad will be presenting their work in Number Theory, Combinatorics and allied areas as invited talks. Paper presentation sessions for budding researchers to present their work are also included. Original and unpublished work in Number Theory and Combinatorics is invited for presentation. Abstracts not exceeding 500 words bringing out the relevant aspects of the work should be forwarded to the convenor on or before October 31, The authors will be intimated of the acceptance of papers on or before November 15, Full papers in IEEE format and not exceeding 3000 words should reach the convenor before December 01, PROCEEDINGS The proceedings to be brought out as a part of conference will consist of all the invited talks and the papers presented. REGISTRATION FEE Category Student Academician/ Researcher Corporate Pre Registration Registration (Before 01 Dec 2006) (On/After 01 Dec 2006) Indian (Rs.) Foreign (US $) Indian (Rs.) Foreign (US $) If adequate grants are forthcoming, TA(II Class sleeper) / DA will be paid to those who present papers and to a limited number of participants only. IMPORTANT DATES Paper Submission : October 31, 2006 Intimation of paper acceptance : November 15, 2006 Camera ready paper submission & Registration : December 01, 2006 Conference : December 19-22, 2006

5 LIST OF PROBABLE SPEAKERS Prof. Asha Rao, RMIT, Australia. Prof. Carsten Thomassen, Technical University of Denmark. Prof. Cilanne Boulet, Cornell University, USA. Prof. Courcelle, B., University of Bordeaux 1, France. Prof. Gopalakrishnan, K., East Carolina University, USA. Prof. Gutin, G., Royal Holloway, University of London, U.K Prof. Hamza Yesilyurt, University of Florida, USA. Prof. James Haglund, Ohio State University, USA. Prof. Jayaram Sethuram, Florida State University, USA. Prof. Kathrin Bringman, University of Wisconsin, USA. Prof. Krishnaswami Alladi, University of Florida, USA. Prof. Miklos Bona, University of Florida, USA. Prof. Mukthi Acharya, Delhi College of Engg., Delhi, India. Prof. Renu Laskar, Clemson University, USA. Prof. Vijayakumar, G.R., TIFR, Mumbai, India. SASTRA Ramanujan Award Winner PATRONS Shri Arjun Singh Chief Patron Minister for Human Resource Development, Government of India Dr. M. Karunanidhi Hon'ble Chief Minister of Tamil Nadu, India Dr. R. Chidambaram Principal Scientific Advisor to the Government of India Dr. T. Ramasami Secretary, Department of Science and Technology, New Delhi, India Prof. S.K. Thorat Chairman, University Grants Commission, New Delhi, India Prof. Damodar Acharya Chairman, All India Council for Technical Education, New Delhi, India Dr. A. Sivathanu Pillai Distinguished Scientist & Chief Controller R & D DRDO, India Dr. Katepalli R. Srinivasan Director, Abdus Salam International Centre for Theoretical Physics, Italy Prof. R. Sethuraman ADVISORY COMMITTEE: Dr. Acharya, B.D. Scientist, DST, New Delhi, India Dr. Krishnaswami Alladi, Chairman Professor and Chairman, Department of Mathematics, University of Florida, USA Dr. Manindra Agarwal Indian Institute of Technology, Kanpur, India Dr. K.S. Chari Senior Director, Ministry of Communications and Information Technology, New Delhi Dr. Vijayaraghavan, M.S. CEO, SETS, Bangalore, India

6 ORGANIZING COMMITTEE Prof. Vaidhyasubramanian, S., Dean (Planning & Development). Prof. Swaminathan, S., Dean (Sponsored Research) & Director CeNTAB Prof. Vijayakumar, G.R., Tata Institute of Fundamental Research, Mumbai Prof. Sampath Kumar, E., University of Mysore, Mysore. Shri Anantharaman, N. Registrar, SASTRA. Prof. Ramakrishnan, P.V., Dean (Engineering), SRC, SASTRA. Prof. Ramani, P., Dean (Education), SRC, SASTRA. Prof. Rajagopalan, L., Department of Mathematics, SRC, SASTRA. Prof. Balakrishnan, R., DST Chair, SRC, SASTRA. Prof. Srinivasa Rao, K., DST Chair, SRC, SASTRA. Prof. Thiyagaragan, M., Department of Mathematics, SASTRA. Prof. Kannan, K., Department of Mathematics, SASTRA. Prof. Srinivasan, V., Department of Commerce, SRC, SASTRA. Prof. Badrinath, V., Department of Commerce, SRC, SASTRA. Prof. Chandrasekar, V., Department of ECE, SRC, SASTRA. ABOUT SASTRA SHANMUGHA ARTS, SCIENCE, TECHNOLOGY & RESEARCH ACADEMY (SASTRA), established in the year 1984 as Shanmugha College of Engineering, was conferred the status of a Deemed University in the year Right from its inception, SASTRA has achieved national standing in terms of academic performance, co - curricular and extra-curricular activities and also in the growth and commitment to social service. SASTRA offers various undergraduate, postgraduate and doctoral programmes in Engineering, Arts, Science and Management. The excellence of the academic programmes offered by the University is reflected in the ratings awarded by National Assessment and Accreditation Council (NAAC), the high grades received from the National Board of Accreditation (NBA) and the success of its students in both industry and academia. SASTRA has established synergetic relationships with international universities like Carnegie Mellon University, USA, Nanyang Technological University, Singapore, Swiss German University, Indonesia, University of Arkansas, USA and with research centres worldwide. SASTRA has established Srinivasa Ramanujan Centre as a tribute to Srinivasa Ramanujan, the great mathematician who lived at Kumbakonam. THE VENUE The international conference is being organized at Srinivasa Ramanujan Centre, an off campus centre of SASTRA at Kumbakonam. The centre housed in a six storeyed structure with spacious class rooms, well stocked library, state-of-the-art laboratories and

7 computer centre provides a congenial atmosphere for those in pursuit of academic excellence. This centre also houses a museum, called House of Ramanujan, on the life and works of Srinivasa Ramanujan. SASTRA purchased the house where Srinivasa Ramanujan lived and renovated it. The house and the museum have been dedicated to the nation by His Excellency, Dr. A.P.J. Abdul Kalam, President of India. DST has established two chairs for research in Discrete Mathematics and Ramanujan Mathematics respectively. ABOUT KUMBAKONAM Kumbakonam, the historic and holy city with hoary traditions is the venue of the conference. Situated between two rivers, the Cauvery and the Arasalar, it is rich in invaluable inscriptions, sculptures and Hindu architecture which speak about its ancient glory, dating back to the Sangam Age. Its close association with two great schools of Hinduism namely Saivism and Vaishnavism, its famous temples, its palaces and institutions, both scholastic and philanthropic, its reputation for fostering both Sanskrit and Tamil culture, epitomizes the best in tradition of South Indian culture. Besides Srinivasa Ramanujan, Kumbakonam can boast of intellectual stalwarts like Rt. Hon'ble V.S.Srinivasa Sastri and Dr. U.V. Swaminatha Iyer, known the world over for their extraordinary mastery and contribution to English and Tamil. This busy commercial and agricultural centre, 37km North-East of Thanjavur is well known for its sacred Mahamaham festival celebrated once in 12 years when the Sun enters the constellation of Aquarius and Jupiter enters Leo. The year 2004, marked the most recent Mahamaham festival in Kumbakonam. Chennai, the Major International Airport is at a distance of 300 Kms. from this town and is well connected by rail and road. SPONSORSHIP Platinum Sponsor Rs 75,000 $2000 One full page colour advertisement in the Conference Souvenir 4 free passes to the Conference Literature with the registration kit Company Banner on the stage and at prominent places in the conference venue Link to the website Gold Sponsor Rs 50,000 $1500 One full page colour advertisement in the Conference Souvenir 3 free passes to the Conference Literature with the registration kit Company Banner at two prominent places in the conference venue

8 Silver Sponsor Rs. 35,000 $ 1000 One full page colour advertisement in the Conference Souvenir 2 free passes to the Conference Literature with the registration kit Company Banner at a prominent place in the conference venue ADVERTISEMENT CHARGES Location Back Cover Inside front & Inside Back Full Page (Colour) Full Page(Black&White) Half Page(Black &White) Size 7 x 10 7 x 10 7 x 10 7 x 10 7 x 4.5 Amount Rs. $US 25,000 15,000 10,000 7,500 5, CONTACT INFORMATION Dr. K. Chandrasekhara Rao, Convenor INTERNATIONAL CONFERENCE ON NUMBER THEORY & COMBINATORICS" SRINIVASA RAMANUJAN CENTRE SASTRA Deemed University, Kumbakonam , INDIA. Phone : , Fax : E mail : icntc@sastra.edu Web site : SRINIVASA RAMANUJAN CENTRE

9 INTERNATIONAL CONFERENCE on NUMBER THEORY & COMBINATORICS DECEMBER 2006 Name (in Block letters) : Designation : Institution : REGISTRATION FORM Tel. No. : Fax No. Address for Correspondence : Tel. No. : Fax No. DD No. : Date : Bank : Signature with date Signature of Sponsoring authority with seal * Students should include a Bonafide Certificate from their institution.

10 To Dr. K. Chandrasekhara Rao, Convenor INTERNATIONAL CONFERENCE ON NUMBER THEORY & COMBINATORICS" SRINIVASA RAMANUJAN CENTRE SASTRA Deemed University, Kumbakonam , INDIA. Fax : E mail : icntc@sastra.edu