1. Linear Sequential Dynamical Systems and the Moebius Functions of Partially Ordered Sets
Ricky X. F. Chen (joint work with C. Reidys)
In this project, linear SDS are investigated. We will see that a linear SDS is completely determined by a matrix in which the sequential updating schedule is implicitly encoded,
A close connection to the incidence algebra of posets was observed, which leads to
a cut theorem of posets.
Linear Sequential Dynamical Systems
Compute the System Map
A Cut Theorem of Posets
Connection to the incidence algebra of posets
Conclusion:
Linear SDS and their close connections to the incidence algebra of posets were investigated. Further work on the homogeneous chain decomposition of posets is ongoing.
References:
[1] R. Chen, C. Reidys (2015), Linear sequential dynamical systems and the Moebius functions of partially ordered sets, under review.
[2] R. Chen, Homogeneous chain decompositions of partially ordered sets, in preparation.
SIAM Conference on Discrete Mathematics 2016