Power series representing Posets

Consider the category of finite posets with a unique maximum and a unique minimum. We prove that two geometrically inspired operations on this category are transported to labeling series. Consequently, we prove new identities of binomial coeficients. We provide an algorithm to determine if a power series is associated to a certain family of posets. We compute the number of labeling functions for a family of posets.Comment: 39 pages. We added an application to Probability. Grammar errors correcte

Polychrony as Chinampas

We study the flow of signals through paths with the following condition: a node emits a signal if two incoming signals from other nodes arrive coincidentally or if it receives an external stimuli. We apply our study to count and describe families of polychrony groups on a line, and we introduce triangular sequences.Comment: 32 pages. We refocus our study on nonlinear signal-flow graphs. We add possible generalizations of our wor