The Independent Even Factor Problem

2008 ◽  
Vol 22 (4) ◽  
pp. 1411-1427 ◽  
Author(s):  
Satoru Iwata ◽  
Kenjiro Takazawa
Keyword(s):  
Factor Problem ◽  
Even Factor

scholarly journals Towards a Resolution of the Proton Form Factor Problem: New Electron and Positron Scattering Data

2015 ◽  
Vol 114 (6) ◽  
Author(s):  
D. Adikaram ◽  
D. Rimal ◽  
L. B. Weinstein ◽  
B. Raue ◽  
P. Khetarpal ◽  
...  
Keyword(s):  
Form Factor ◽  
Scattering Data ◽  
Proton Form Factor ◽  
Positron Scattering ◽  
Proton Form ◽  
Factor Problem

The factor problem.

2004 ◽  
pp. 44-69
Author(s):  
L. L. Thurstone
Keyword(s):  
Factor Problem

A weighted even factor algorithm

2007 ◽  
Vol 115 (2) ◽  
pp. 223-237 ◽  
Author(s):  
Kenjiro Takazawa
Keyword(s):  
Even Factor

scholarly journals ON THE COMPLEXITY OF THE WHITEHEAD MINIMIZATION PROBLEM

2007 ◽  
Vol 17 (08) ◽  
pp. 1611-1634 ◽  
Author(s):  
ABDÓ ROIG ◽  
ENRIC VENTURA ◽  
PASCAL WEIL
Keyword(s):  
Free Group ◽  
Polynomial Time ◽  
Minimization Problem ◽  
Finite Rank ◽  
Polynomial Algorithm ◽  
Minimum Size ◽  
Input Word ◽  
Finitely Generated ◽  
Factor Problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem — to decide whether a word is an element of some basis of the free group — and the free factor problem can also be solved in polynomial time.

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