Topological multidimensional van der Waerden theorem
Two congruences involving 4-cores.
Two sided Sand Piles Model and unimodal sequences
We introduce natural generalizations of two well-known dynamical systems, the Sand Piles Model and the Brylawski's model. We describe their order structure, their reachable configuration's characterization, their fixed points and their maximal and minimal length's chains. Finally, we present an induced model generating the set of unimodal sequences which amongst other corollaries, implies that this set is equipped with a lattice structure.