scholarly journals Tight lower bounds for the longest common extension problem

2017 ◽  
Vol 125 ◽  
pp. 26-29
Author(s):  
Dmitry Kosolobov
Keyword(s):  
Lower Bounds ◽  
Extension Problem ◽  
Common Extension

scholarly journals The Lifting-Extension Problem for Duchain Complexes of Dwyer and Kan

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
Jan Spaliński
Keyword(s):  
Commutative Diagram ◽  
Chain Complex ◽  
Category Structure ◽  
Extension Problem ◽  
Weak Equivalence ◽  
Cochain Complex ◽  
Common Extension ◽  
A Chain ◽  
The Right ◽  
Countably Infinite

AbstractA duchain complex of W. Dwyer and D. Kan is a common extension of the notions of a chain complex and a cochain complex.Given a square commutative diagram of duchain complexes, the lifting-extension problem asks whether there exists a diagonal map making the two resulting triangles commute. Duchain complexes have a model category structure, and hence a lift exists if the left vertical map is a cofibration, the right vertical map is a fibration, and one of them is a weak equivalence.We show that it is possible to replace the two conditions above, by a countably infinite, bigraded, family of conditions which guarantee the existence of a lift.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds
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