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GENERALISED STACK PERMUTATIONS M D Atkinson
 

Summary: GENERALISED STACK PERMUTATIONS
M D Atkinson
School of Mathematical and Computational Sciences
North Haugh, St Andrews, Fife KY16 9SS
Abstract
Stacks which allow elements to be pushed into any of the top r posi-
tions and popped from any of the top s positions are studied. An asymp-
totic formula for the number un of permutations of length n sortable by
such a stack is found in the cases r = 1 or s = 1. This formula is found
from the generating function of un . The sortable permutations are char-
acterised if r = 1 or s = 1 or r = s = 2 by a forbidden subsequence
condition.
1 Introduction
Let  = [ 1 ;  2 ; : : : ; n ] be a permutation of 1; 2 : : : ; n appearing as the input
stream to a stack. If, through an appropriate series of push and pop operations,
the stack can discharge the input elements in the order 1; 2 : : : ; n then  is
said to be a stack sortable permutation. Stack sortable permutations were rst
investigated by Knuth in [4], section 2.2.1, and it was proved that there are
2n
n

  

Source: Atkinson, Mike - Department of Computer Science, University of Otago

 

Collections: Computer Technologies and Information Sciences