3,718 research outputs found
Permutations generated by a stack of depth 2 and an infinite stack in series
We prove that the set of permutations generated by a stack of depth two and an innite stack in series has a basis (dening set of forbidden patterns) consisting of 20 permutations of length 5, 6, 7 and 8. We prove this via a \canonical" generating algorithm
Permutations generated by a depth 2 stack and an infinite stack in series are algebraic
© 2015, Australian National University. All rights reserved. We prove that the class of permutations generated by passing an ordered sequence 12... n through a stack of depth 2 and an in nite stack in series is in bi-jection with an unambiguous context-free language, where a permutation of length n is encoded by a string of length 3n. It follows that the sequence counting the number of permutations of each length has an algebraic generating function. We use the explicit context-free grammar to compute the generating function:(formula presented) where cn is the number of permutations of length n that can be generated, and (formula presented) is a simple variant of the Catalan generating function. This in turn implies that (formula presented
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-stack sortable permutations and show that these two classes are
closely related. Moreover, we give an optimal O(n^2) algorithm to decide if a
given permutation of size n is 2-stack pushall sortable and describe all its
sortings. This result is a step to the solve the general 2-stack sorting
problem in polynomial time.Comment: 41 page
Molecular Dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition
In this paper we describe a version of London Langevin molecular dynamics
simulations that allows for investigations of the vortex lattice melting
transition in the highly anisotropic high-temperature superconductor material
BiSrCaCuO. We include the full electromagnetic
interaction as well as the Josephson interaction among pancake vortices. We
also implement periodic boundary conditions in all directions, including the
z-axis along which the magnetic field is applied. We show how to implement flux
cutting and reconnection as an analog to permutations in the multilevel Monte
Carlo scheme and demonstrate that this process leads to flux entanglement that
proliferates in the vortex liquid phase. The first-order melting transition of
the vortex lattice is observed to be in excellent agreement with previous
multilevel Monte Carlo simulations.Comment: 4 figure
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