The Shifted Turán Sieve Method on Tournaments. Issue 4 (December 2019) - Kuo, Wentang; Liu, Yu-Ru; Ribas, Sávio; Zhou, Kevin
Abstract: We construct a shifted version of the Turán sieve method developed by R. Murty and the second author and apply it to counting problems on tournaments. More precisely, we obtain upper bounds for the number of tournaments which contain a fixed number of restricted $r$ -cycles. These are the first concrete results which count the number of cycles over "all tournaments".