Matrix representation of meet-irreducible discrete copulas

Following Aguiló–Suñer–Torrens (2008), Kolesárová–Mesiar–Mordelová–Sempi (2006) and Mayor–Suñer–Torrens (2005), we continue to develop a theory of matrix representation for discrete copulas. To be more precise, we give characterizations of meet-irreducible discrete copulas from an order-theoretical aspect: we show that the set of all irreducible discrete copulas is a lattice in analogy with Nelsen and Úbeda-Flores (2005). Moreover, we clarify its lattice structure related to Kendallʼs τ and Spearmanʼs ρ borrowing ideas from Coxeter groups.