Juarna, Asep and Vajnovszki, Vincent Some generalizations of a simionschmidt bijection. Skripsi Program Studi Psikologi.

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SOME GENERALIZATIONS OF A SIMIONSCHMIDT BIJECTION_UG.pdf  Submitted Version Download (208Kb)  Preview 
Abstract
In 1985 Simion and Schmidt gave a constructive bijection 4 from the set of all length (n — 1) binary strings having no two consecutive is to the set of all length n permutations avoiding all patterns in {123, 132,213). In this paper we generalize 4 to an inject ive function from {O, i}n_1 to the set S, of all length n permutations and derive from it four bijections : P —* Q where P ç {O, i}?_1 and Q C S,. The doniaiiis are sets of restricted binary strings and the codomains are sets of patternavoiding permutations. As a particular case we retrieve the original SimionSchmidt bij ect ion. We also show that the l)ijections obtained are actually combinatorial isomorphisms, i.e., closeness—preserving bijections. Three of them have known Cray codes and generating alg orithms for their domains and we present similar results for each corresponding codomain, under the appropriate combinatorial isomorphism.
Item Type:  Article 

Uncontrolled Keywords:  patternavoiding permutations; fibonacciand lucas string; constructive bijection; combinational; gray codes 
Subjects:  A General Works > AI Indexes (General) 
Divisions:  Fakultas Psikologi > Program Studi Psikologi 
Depositing User:  Mr Reza Chandra 
Date Deposited:  25 Feb 2014 04:51 
Last Modified:  25 Feb 2014 04:51 
URI:  http://repository.gunadarma.ac.id/id/eprint/57 
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