منابع مشابه
2-stack Pushall Sortable Permutations
In the 60’s, Knuth introduced stack-sorting and serial compositions of stacks. In particular, one significant question arise out of the work of Knuth: how to decide efficiently if a given permutation is sortable with 2 stacks in series? Whether this problem is polynomial or NP-complete is still unanswered yet. In this article we introduce 2-stack pushall permutations which form a subclass of 2-...
متن کاملGeneralizations of Two-stack-sortable Permutations
i iii Acknowledgment My deepest gratitude goes to my advisor, Ira Gessel, without whom this work would not be possible; I would like to thank him for his generosity in sharing his insight and time with me, and his constant patience and encouragement. It was and will always be my pleasure to work with him.
متن کاملOn the Stack Sortable and Pushpopable Permutations
This work proposes an O(log n) time parallel algorithm for testing whether a permutation is stack sortable or not by O(n) processors under the PRAM EREW computational model. Additionally, the number of permutations which are both stack sortable and pushpopable is also discussed, and an equality is finally obtained, which combines n!, 2, Cn, and Un together where Cn is the Catalan number and Un ...
متن کامل2-stack Sortable Permutations with a given Number of Runs
Using earlier results we prove a formula for the number W(n,k) of 2stack sortable permutations of length n with k runs, or in other words, k − 1 descents. This formula will yield the suprising fact that there are as many 2-stack sortable permutations with k−1 descents as with k−1 ascents. We also prove that W(n,k) is unimodal in k, for any fixed n.
متن کاملA Wilf Equivalence Related to Two Stack Sortable Permutations
A permutation is so-called two stack sortable if it (i) avoids the (scattered) pattern 2-3-4-1, and (ii) contains a 3-2-4-1 pattern only as part of a 3-5-2-4-1 pattern. Here we show that the permutations on [n] satisfying condition (ii) alone are equinumerous with the permutations on [n] that avoid the mixed scattered/consecutive pattern 31-4-2. The proof uses a known bijection from 3-2-1-avoid...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2020.105209