All Questions

For a certain commutative semigroup of integer size $n$, $G=(\{1,2,\dots,n\},\circ: x\circ y\mapsto \min(n,x+y))$, consider all complex functions on it, denoted by $\mathbb C[G]$ or $\mathbb CG$. ...

I have found some functions $t_g, g \in G$ for cyclic groups $G=C_n$ which seem to satisfy the following convolution identity: $$t_g(x+y) = \sum_{h \in G} t_{gh^{-1}}(x) t_h(y)$$ Example of such ...