Max over k in Viterbi forward pass formulation

The notation “max over k” looks confusing. As I understand, this “k” has nothing to do with the total number of words “K”; it is rather “max over tag n” – am I understanding it correctly?

Yeah you’re understanding it correctly. The lower case “k” is just a parameter we’re using to traverse over tags. I understand it can be confusing though. I’ll bring up the suggestion to the team