Summary: Part I
THE PERMUTATIONAL POWER OF A PRIORITY QUEUE
M. D. ATKINSON* and MURALI THIYAGARAJAH
Department ofMathematical and School of Computer Science,
Computational Sciences, Carleton University,Ottawa,
North Haugh, St. Andrews, Canada KIS 5B6
Fife K Y16 9SS, Scotland
A priority queue transforms an input permutation crof some set of size n into an output permutation z.
It is shown that the number of such pairs (a, z) is (n + 1)"- 1 Some related enumerative and algorithmic
questions are also considered.
Keywords: Priority queue, permutation, enumeration.
CR Categories:E. 1, G.2.1.
Priority Queues are abstract data types which support the operations: Insert,
Delete-Minimum. They have many applications and several efficient implementa-
tions of them are known. In this paper we shall be concerned with the effect of
a priority queue on the order of the data items that pass through it. Suppose that
al, a2,..., a,, is some stream of input to a priority queue. Each Insert operation