In this talk, I will present a use of Borsuk-Ulam Theorem which solves a discrete problem called the ”splitting necklace problem”. A similar technique allows to prove that the word problem of Zn can be solved by a multiple context-free grammar. Instead of following this proof, we turn to a combinatorial equivalent of Borsuk-Ulam Theorem, Tucker’s Lemma (more precisely the octahedral Tucker lemma). We present a proof that the P`alvo ̈lgyi of the ”splitting necklace problem”. We then show how to adapt this proof so as to show that the word problem in Z
n can be solved by a multiple context-free grammar.
Emploi du temps
ICI
Comment arrivé à l'IMT?
IMT's address is the following :
118 Route de Narbonne
31062
Toulouse
The nearest Metro Station is "Université Paul Sabatier" on the yellow metro line (Metro B).
From the Airport : You can :
- Take a taxi (the cost depends on the traffic load and on the hour but you should expect to spend between 40 and 65 euros approximately)
- Or take the "Navette Tisseo" in front of the arrivals of the airport (it is a bus which leaves every 20 minutes approximately), get down at the stop "Compans Cafarelli" and take the Metro Line B (yellow line) in direction "Ramonville" and stop at "Université Paul Sabatier". The ticket for the "Navette" can be bought at the box office at the exit of the arrivals of the Airport.
- Or you can take the Tram line 1 (leaving in front of the arrival of the airport), get down at the terminus ("Palais de Justice") and from there take the metro line 2 (yellow line) in direction "Ramonville" and stop at "Université Paul Sabatier". The ticket of the tram can be bought at the machins in front of the tram.
From the station "Gare Matabiau" :
Take the metro line A (red line) in direction "Basso Cambo" and get down at "Jean Jaurés" (just one stop) then change and take the metro line B (yellow line) in direction "Ramonville" and get down at "Université Paul Sabatier".
Once you are at the metro station "Université Paul Sabatier", you are at approximately 200 m from IMT : the main building of IMT is the building 1R2, in the grid of the campus map it is in the square C4. See the map of the campus here below :
Plan of the Campus
The closest airport is
Toulouse Blagnac (TLS), with many flights to european cities and a few intercontinental ones. The centre is conveniently reached with the
airport shuttle.
The university can be reached using the Metro B line, stop at "Université Paul Sabatier"; the maths department is in buildings
1R1,1R2,1R3.