Permutation codes, source coding and a generalisation of   Bollob\'as-Lubell-Yamamoto-Meshalkin and Kraft inequalities
  We develop a general framework to prove Kraft-type inequalities for prefix-free permutation codes for source coding with various notions of permutation code and prefix. We also show that the McMillan-type converse theorem in most of these cases does not hold, and give a general form of a counterexample. Our approach is more general and works for other structures besides permutation codes. The classical Kraft inequality for prefix-free codes as well as results about permutation codes follow as corollaries of our main theorem and main counterexample. 
Kristo Visk and Ago-Erik Riet
cs.IT math.CO math.IT