Cm Elliptic Curves and Bicolorings of Steiner Triple Systems |
| |
Authors: | Dummit David S |
| |
Institution: | Department of Mathematics, University of Vermont Burlington, VT 05401, USA; dummit{at}math.uvm.edu |
| |
Abstract: | It is shown that a necessary condition for the existence ofa bicolored Steiner triple system of order n is that n can bewritten in the form A2+3B2 for integers A and B. In the casewhen n=q is either a prime congruent to 1 mod 3, or the squareof a prime congruent to 2 mod 3, it is shown that the numbersof colored vertices in the triple system would be unique, andare given by the number of points on specific twists of theCM elliptic curve y2=x31 over the finite field Fq. 2000Mathematics Subject Classification 05B07, 11G20, 14G15 (primary);11G15, 14K22 (secondary). |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|