detect subset in series

Dear R Users, I am curious whether there is any simple solution o my  
problem.

My example 'series':
series <- c(1,1,1,0,1,0,0,1,1,0,0,0,0,1)

My 'subset' of interest:
subset <- c(0,0,0,0)

Is there any function which tells me that the subset exists in my  
series,
and gives me position where in series is starts. In provided example  
the
subset exists and covers the elements 10:13 of the 'series'.