A note on Möbius algebras and applications

We show a diagonalisation variant of Lindström calculation method. As an application of this result we calculate the dimension of the affine space of Negami's splitting matrices. We do so by writing down an expression for the Möbius function in term of Möbius algebra identities. As a corollary we get Lindström's result in a self contained way. Finally, we calculate the partition lattice characteristic polynomial via the Negami's polynomial.