相关论文: Fertilitopes

The polytope subalgebra of deformations of a zonotope can be endowed with the structure of a module over the Tits algebra of the corresponding hyperplane arrangement. We explore this construction and find relations between statistics on…

We consider closed orientable surfaces $S$ of genus $g>1$ and homeomorphisms $f:S\rightarrow S$ homotopic to the identity. A set of hypotheses is presented, called fully essential system of curves $\mathscr{C}$ and it is shown that under…

Root systems are sets with remarkable symmetries and therefore they appear in many situations in mathematics. Among others, denominator formulae of root systems are very beautiful and mysterious equations which have several meanings from a…

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…

Let $V$ be a complete discrete valuation ring with fraction field $F$ of characteristic zero and with residue field $\mathbb{F}$. We introduce analytic cyclic homology of complete torsion-free bornological algebras over $V$. We prove that…

We study the category whose objects are trees (with or without roots) and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian, and we study two natural families of modules over…

We introduce an infinitesimal Hopf algebra of planar trees, generalising the construction of the non-commutative Connes-Kreimer Hopf algebra. A non-degenerate pairing and a dual basis are defined, and a combinatorial interpretation of the…

Split-metric decompositions are an important tool in the theory of phylogenetics, particularly because of the link between the tight span and the class of totally decomposable spaces, a generalization of metric trees whose decomposition…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

We initiate the study of a class of polytopes, which we coin polypositroids, defined to be those polytopes that are simultaneously generalized permutohedra (or polymatroids) and alcoved polytopes. Whereas positroids are the matroids arising…

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…

Let $X$ be a complex manifold, $\pi: E \rightarrow X$ a locally trivial holomorphic fibration with fiber $F$, and $\mathfrak{g}$ a Lie algebra with an invariant symmetric form. We associate to this data a holomorphic prefactorization…

We present an explicit closed-form formula for the vertices of the classical cut polytope $\operatorname{CUT}(n)$, defined as the convex hull of cut vectors of the complete graph $K_n$. Our derivation proceeds via a related polytope,…

Throughout $A$ will denote commutative noetherian ring, with $\dim A=d\geq 2$, and $P$ denote a projective $A$-module with $rank(P)=n$. In \cite{MM1} we considered the Homotopy obstruction sets $\pi_0\left({\mathcal LO}(P)\right)$, which…

In this paper, we study homotopical analogues of the Cantor-Bendixson derivative. For each $n\geq 0$, the "$\pi_n$-wild set" $\mathbf{w}_n(X)$ of a topological space $X$ is the subspace of $X$ consisting of the points at which there exists…

Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This…

This is a sequel paper of arXiv:1306.1466 in which we study the comodules over a regular weak multiplier bialgebra over a field, with a full comultiplication. Replacing the usual notion of coassociative coaction over a (weak) bialgebra, a…

A simple convex polytope $P$ is \emph{cohomologically rigid} if its combinatorial structure is determined by the cohomology ring of a quasitoric manifold over $P$. Not every $P$ has this property, but some important polytopes such as…

We present a new data structure for maintaining dynamic permutations, which we call a $\textit{forest of splay trees (FST)}$. The FST allows one to efficiently maintain the cycle structure of a permutation $\pi$ when the allowed updates are…