Can you give me an example of any PKC encrytion algorithm with coins? I'm reading a Definition of Public Key Encryption and here say:


  ...
  Enc is a (possibly) probabilistic polynomial time encryption algorithm which takes as input a public key $pk$, a $m\in M$ and random coins $r$, and outputs a ciphertext $c\in C$. 


But in other papers, there is no mention of coins $r$.

Can you give me examples of PKC  encrytion algorithms with coins?
All textbook PKC systems are never applied as they are described. Take e.g: RSA.
There is a random padding technique that plays the role of the coins. The coins make the scheme probabilistic. For the same reason a block cipher which is instatiated as a pseudorandom permutations takes as input an instatiation vector IV. OAEP is a commonly used random encoding scheme before applying RSA on your data.