Date of Award
2026
Thesis Access
Open Access Honors Thesis
Thesis Location
Honors College Thesis
Degree Name
B.S.
Department
Computer Science
Faculty Advisor
Andrew Salch
Abstract
This paper introduces Multi-Party Tournament (MPT) designs that generalize established combinatorial structures, including Whist, Pitch, and Generalized Whist tournament designs. This work will formally define MPTs, establish the fundamental properties of resolvability, fullness, and balance, and formulate a mathematical and algorithmic foundation for multi-party tournament scheduling. The primary contributions of this research are the presentation of necessary and sufficient existence conditions for MPTs across various properties and parameters, the identification of connections between MPTs and other fields of mathematics such as combinatorial design theory, graph theory, and probability theory, and the investigation of MPT construction algorithms, including tree-search, finite-field constructions, and combinatorial design constructions. The investigations of the ally-count and rival-count functions, the ally-matrix and rival-matrix, and the induced BIBDs are all significant contributions to MPT theory. The construction techniques offer a versatile toolkit to construct Balanced Multi-Party Tournaments across various properties and parameters, and the explored constructions for specific formats, such as Euchre (Eu(v, r)) and Pitch (Pitch(v)), illustrate the practical utility of MPT theory in solving real-world scheduling challenges. Ultimately, this paper provides a general solution to the challenge of creating a balanced schedule for games, such as Euchre or Pitch, with arbitrary team sizes and player counts.
Recommended Citation
Nematollahe, Parsa, "Balanced Multi-Party Tournament Designs" (2026). Honors College Theses. 97.
https://digitalcommons.wayne.edu/honorstheses/97
Included in
Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons, Theory and Algorithms Commons