I am reading this paper named "Matching triangles and basing hardness on an extremely popular conjecture" in the second page of this paper there is this paragraph:
Observe that the ∆-Matching-Triangles problem with ∆ = 1 simply asks if there is a triangle in the graph and can, therefore, be solved in O(n^ω) time, where ω < 2.373 is the matrix multiplication exponent, However, when ∆ increases to ω(1) it must require n3−o(1) time under Conjecture 1...
can anyone explain to me what does the "w(1)" mentioned there mean? I am new to this. I have figured all the other symbols and what they mean but I can't quite get my head around the w(1).
This is the link to the paper for further investigation: https://people.csail.mit.edu/virgi/MatchTria.pdf
Thank you.