Permutations generated by stacks and deques

نویسندگان

  • M. H. Albert
  • M. D. Atkinson
  • S. A. Linton
چکیده

Lower and upper bounds are given for the the number of permutations of length n generated by two stacks in series, two stacks in parallel, and a general deque.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Permutations sortable by deques and by two stacks in parallel

In his seminal work The Art of Computer Programming [2], Knuth was the first to consider a number of classic data structures from the point of view of the permutations they could produce from the identity permutation, or equinumerously, the permutations which the data structure can sort. Famously, he noticed that the permutations obtainable using a single stack are exactly those which avoid the...

متن کامل

Practical Memory Checkers for Stacks, Queues and Deques

A memory checker for a data structure provides a method to check that the output of the data structure operations is consistent with the input even if the data is stored on some insecure medium. In 8] we present a general solution for all data structures that are based on insert(i; v) and delete(j) commands. In particular this includes stacks, queues, deques (double-ended queues) and lists. Her...

متن کامل

Recent Results in Pattern-avoiding Permutations

In the late 1960s Don Knuth asked which permutations could be sorted by various data structures. For a simple stack, he proved that permutations avoiding the pattern 312 can be so sorted, and further, that the number of such permutations of length n is given by Cn, the n th Catalan number. Knuth went on to pose the same question about other data structures that are widely used in sorting operat...

متن کامل

Comparing algorithms for sorting with t stacks in series

We show that the left-greedy algorithm is a better algorithm than the right-greedy algorithm for sorting permutations using t stacks in series when t > 1. We also supply a method for constructing some permutations that can be sorted by t stacks in series and from this get a lower bound on the number of permutations of length n that are sortable by t stacks in series. Finally we show that the le...

متن کامل

Expander Graphs, Strong Ergodicity, and Superstrong Approximation

After introducing expander graphs and briefly discussing classical results and constructions, I will talk about recent developments pertaining to establishing expansion property for congruence quotients of thin groups –discrete subgroups of semi-simple groups which are Zariski dense but of infinite index. This expansion property is intimately related to strong ergodicity of the associated group...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009