Following, we present in this paper various number encodings and operations over multisets. We obtain the most compact encoding and several other interesting
encodings and study their properties using elements of combinatorics over multisets. We
also construct P systems that implement their associated operations. We quantify the effect of adding order to a multiset thus obtaining a string, as going from encoding lengths
of the number n in base b and time complexities of operations of the order b
p
n to lengths
and complexities of order logbn:
