About a question of Gateva-Ivanova and Cameron

Postato il

April 10, 2019
11.00 – 13.00 – Aula M5
Marco Castelli

In 2011 Gateva-Ivanova and Cameron [2], following a suggestion due by P. Martin, posed the following question:

Question. For each positive integer m denote by N_m the minimal integer so that there exists a square-free involutive multipermutational solution (X_m,r_m) of order |X_m| = N_m and with mpl(X_m, r_m) = m. How does N_m depend on m?

They showed [2] that N_m \geq 2^{m-1} + 1 for every m \in N and, some years later, Lebed and Vendramin improve [3] the estimation showing indirectly that N_m \leq 2^{m-2} for every m > 4. In this talk we will present some recent results obtained in [1] that allow us to improve the estimation of the sequence N_m.