# What does “$:[$” mean in $q_{(i,d,j)} ≜ P(S_{[t+1:t+d]}=j\;|S_{[t+1:[}=j)$?

I am reading through some math on a paper, and I am trying to properly understand some of the proofs / equations. In particular, $$q_{(i,d,j)} ≜ P(S_{[t+1:t+d]}=j|S_{[t+1:[}=j)$$ is fairly confusing to me.

I know that the function q is being defined as that following block, and so on, but I am getting lost at what :[ means. Does anyone know where to point me? Google comes up with nothing on this notation, though I am aware that [] is used to typically denote arrays / sets.

Paper in question is here (formula on page 5)

• Possibly related might be notation borrowed from computer programming... given an array, myarray = [a,b,c,d,e,f,g] the notation myarray[2:4] would return the subarray which starts at and includes the second entry and ends at but doesn't include the fourth entry, in this case myarray[2:4] returns [c,d] (arrays start counting from 0). If a colon appears without anything to the left or right of it, it is unbounded in that direction, for example myarray[3:] returns [d,e,f,g]. At a glance it appears as though a similar meaning might be intended here. – JMoravitz Jan 26 at 0:28