VIETNAM ACADEMY OF SCIENCE AND TECHNOLOGY INSTITUTE OF MATHEMATICS SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom – Happiness ABSTRACT OF Ph D THESIS Title Characterizations of the configuration[.]
Trang 1VIETNAM ACADEMY OF
SCIENCE AND TECHNOLOGY
INSTITUTE OF MATHEMATICS
-SOCIALIST REPUBLIC OF VIETNAM Independence – Freedom – Happiness
ABSTRACT OF Ph.D THESIS Title: Characterizations of the configuration spaces and the stability of some extended sandpile
models
Speciality: Mathematical Foundations of Computer science
Code: 62 46 01 10
PhD student: Trần Thị Thu Hương
Advisor: Assoc Prof Dr Phan Thị Hà Dương
Training institute: Institute of Mathematics – Vietnam Academy of Science and Technology Abstract: The manuscript presents some generalizations of two discrete dynamical systems:
Sandpile model (SPM) and Chip firing game (CFG) We focus on the reachabilities, the time to reach stable configurations and the configuration spaces on these generalized systems
1 The extended SPM: We add grains on random columns of stable configurations of SPM
We prove that the infinite set of all stable configurations have a lattice structure which is
a sublattice of Young lattice We give an explicit formula for the smallest and the greatest time to reach stable configurations in the system
2 The parallel symmetric SPM: We prove that the forms of fixed points of the parallel model and the sequential model are the same Moreover, our proof is a constructive one which gives a nearly shortest way to reach a given fixed point form
Scientific advisor Phan Thị Hà Dương
Ph.D student Trần Thị Thu Hương
3 The signed CFG: We show an isomorphism between symmetric SPM and signed CFG when the supported graph is either cycles or the infinite line Therefore, we give a characterization of reachable configurations and of fixed points of each model At the end, we give explicit formulae for the number of their fixed points