# Pound notation in Summation

I was going through a paper comparing glove and word2vec. I came across the pound notation shown below. What does it mean when used like this? The link for paper is here

In the third paragraph of the first section (page 1), they define $\#(w)$, $\#(w; c)$, and $\#(c)$. Quoting such paragraph:
Word-context pairs are denoted as $(w; c)$, and $\#(w; c)$ counts all observations of $(w; c)$ from the corpus. We use $\#( w ) = \sum_c \#(w; c)$ and $\#(c) = \sum_w \#(w; c)$ to refer to the count of occurrences of a word (context) in all word-context pairs. Either $\sum_c \#(c)$ or $\sum_w \#(w)$ may represent the count of all word-context pairs.
1. $\#(w_i, c_j)$ counts the occurrences of a specific word $w_i$ over the context $c_j$;
2. and $\frac{\#(c_)}{\sum_w \#(w)}$ accounts for the the probability of having context $c_j$ in the dataset.
• But for $$#(w_i, c_j)$$ I couldnt figure out what it is because this is loss for a specific pair of words. So why count in there Apr 30, 2015 at 17:18