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Some New Results on Z ‐Cyclic Patterned Starter Whist Tournaments and Related Frames
Author(s) -
Hu Sihuang,
Ge Gennian
Publication year - 2013
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21313
Subject(s) - tournament , starter , mathematics , construct (python library) , combinatorics , computer science , chemistry , food science , programming language
Abstract The whist tournament problem was introduced by Moore in 1896. To construct Z ‐cyclic whist tournaments, Z ‐cyclic patterned starter whist tournaments were introduced. The systematic research on Z ‐cyclic patterned starter whist tournaments dates back to 1954. Recently, Z ‐cyclic patterned starter whist tournament frames were shown to be instrumental in the constructions of Z ‐cyclic patterned starter whist tournaments. In this paper, we develop some necessary conditions for the existence of Z ‐cyclic patterned starter whist tournament frames and some new necessary conditions for the existence of Z ‐cyclic patterned starter whist tournaments. An infinite family of Z ‐cyclic patterned starter whist tournament frames is constructed through Weil's theorem on character sums. As a consequence, a new infinite family of Z ‐cyclic patterned starter whist tournaments is obtained. In addition, we also give a near complete solution to the existence of Z ‐cyclic patterned starter whist tournaments on no greater than 300 players.