The orientation morphism $Or(\cdot)(P)\colon \gamma\mapsto\dot{P}$ associates differential-polynomial flows $\dot{P}=Q(P)$ on spaces of bi-vectors $P$ finite-dimensional affine manifolds $N^d$ with (sums of) finite unoriented graphs $\gamma$ ordered sets edges and without multiple one-cycles. It is known that $d$-cocycles $\boldsymbol{\gamma}\in\ker d$ respect to the vertex-expanding differenti...

Given a nite graded poset with labeled Hasse diagram, we construct a quasi-symmetric generating function for chains whose labels have xed descents. This is a common generalization of a generating function for the ag f-vector de-ned by Ehrenborg and of a symmetric function associated to certain edge-labeled posets which arose in the theory of Schubert polynomials. We show this construction gives...

Abstract Let $f:X\to X $ be a dominant self-morphism of an algebraic variety. Consider the set $\Sigma _{f^{\infty }}$ $f$-periodic subvarieties small dynamical degree (SDD), subset $S_{f^{\infty maximal elements in }}$, and $S_f$ $f$-invariant }}$. When $X$ is projective, we prove finiteness $P_f$ prime divisors with SDD give optimal upper bound $$\begin{align*} &\sharp P_{f^n}\le d_1(f)^n...

This paper examines the concept of simulation from a modelling viewpoint. How can one Mealy machine simulate the other one? We create formalism for simulation of Mealy machines. The injective s–morphism of the machine semigroups induces the simulation of machines [1]. We present the example of s–morphism such that it is not a homomorphism of semigroups. The story for the surjective s–morphisms ...

A word is cubefree if it contains no non-empty subword of the form xxx. A morphism h : Σ * → Σ * is k-uniform if h(a) has length k for all a ∈ Σ. A morphism is cubefree if it maps cubefree words to cubefree words. We show that for all k ≥ 0 there exists a k-uniform cubefree binary morphism.

Proposition 1.1. (a) Any open immersion is étale. (b) The composite of two étale morphisms is étale. (c) Any base change of an étale morphism is étale. (d) If φ ◦ ψ and φ are étale, then so is ψ. Proposition 1.2. Let f : X → Y be an étale morphism. (a) For all x ∈ X, OX,x and OY,f(x) have the same Krull dimension. (b) The morphism f is quasi-finite. (c) The morphism f is open. (d) If Y is reduc...