Some New Results on inline image-Cyclic Patterned Starter Whist Tournaments and Related Frames

Authors


  • Contract grant sponsors: National Outstanding Youth Science Foundation of China; Contract grant number: 10825103; Contract grant sponsors: National Natural Science Foundation of China; Contract grant number: 61171198; Contract grant sponsors: Specialized Research Fund for the Doctoral Program of Higher Education.

Abstract

The whist tournament problem was introduced by Moore in 1896. To construct inline image-cyclic whist tournaments, inline image-cyclic patterned starter whist tournaments were introduced. The systematic research on inline image-cyclic patterned starter whist tournaments dates back to 1954. Recently, inline image-cyclic patterned starter whist tournament frames were shown to be instrumental in the constructions of inline image-cyclic patterned starter whist tournaments. In this paper, we develop some necessary conditions for the existence of inline image-cyclic patterned starter whist tournament frames and some new necessary conditions for the existence of inline image-cyclic patterned starter whist tournaments. An infinite family of inline image-cyclic patterned starter whist tournament frames is constructed through Weil's theorem on character sums. As a consequence, a new infinite family of inline image-cyclic patterned starter whist tournaments is obtained. In addition, we also give a near complete solution to the existence of inline image-cyclic patterned starter whist tournaments on no greater than 300 players.

Ancillary