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Miao, J., Tao, H., Xie, H., Sun, J. and Cao, J. (2024) Reconstruction-Based Anomaly Detection for Multivariate Time Series Using Contrastive Generative Adversarial Networks. Information Processing & Management, 61, Article ID: 103569. https://doi.org/10.1016/j.ipm.2023.103569

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• TITLE: An Extended Theorem Based on Landau’s Theorem for Facilitating Tournament Score Sequence Reconstruction

  AUTHORS: Bowen Liu

  KEYWORDS: Tournament, Score Sequence, Score Set, Algorithm Design, Reid Conjec-ture

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 29, 2025

  ABSTRACT: The score set of a tournament refers to the collection of its distinct out-degrees. While it is known that for any set of nonnegative integers D , there exists a tournament T with D as its degree set, an efficient algorithm for reconstructing the full score sequence is still lacking. To bridge this gap, this paper focuses on extending the existing Landau’s theorem to establish a new, easily verifiable theorem. By introducing additional constraints beyond Landau’s classical criteria, we aim to offer deeper insights that could facilitate the development of efficient reconstruction algorithms. These findings have practical applications in sports analytics, ranking prediction, and machine learning, particularly in learning-to-rank models and data imputation. In these domains, the ability to reconstruct partial rankings or sequences plays a crucial role in recommendation systems and anomaly detection.