Related papers: Euler's Theorem for Regular CW-Complexes

Given $\alpha>0$ and an integer $\ell\geq5$, we prove that every sufficiently large $3$-uniform hypergraph $H$ on $n$ vertices in which every two vertices are contained in at least $\alpha n$ edges contains a copy of $C_\ell^{-}$, a tight…

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the…

We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent confluence proofs. For this, we introduce the structure of higher globular Kleene algebra, a higher-dimensional generalisation of modal and…

The famous concyclicity theorem stated by John H. Conway is here reconsidered by means of a parametrisation of the associated triangular configuration with arbitrary triplets of real numbers ($\alpha$;$\beta$;$\gamma$). This theorem, thus…

Generalized Pauli's theorem, proved by D. S. Shirokov for two sets of anticommuting elements of a real or complexified Clifford algebra of dimension $2^n$, is extended to the case, when both sets of elements depend smoothly on points of…

Let $K$ be a fixed field. We attach to each column-finite quiver $E$ a von Neumann regular $K$-algebra $Q(E)$ in a functorial way. The algebra $Q(E)$ is a universal localization of the usual path algebra $P(E)$ associated with $E$. The…

Haken n-manifolds have been defined and studied by B. Foozwell and H. Rubinstein in analogy with the classical Haken manifolds of dimension 3, based upon the the theory of boundary patterns developed by K. Johannson. The Euler…

We present results for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-dimensional and two-dimensional series. Most of these series can be expressed in…

In this short note, we introduce an Euler analogue of Wilson's theorem; $a_1a_2... a_{\phi(n)}\equiv (-1)^{\phi(n)+1}~({\rm mod}~n)$ say, where ${\rm gcd}(a_i,n)=1$.

The (over)completeness of even and odd nonlinear charge coherent states is proved and their generation explored. They are demonstrated to be generalized entangled nonlinear coherent states. A $D$-algebra realization of the SU$_f$(1,1)…

Let $\mathscr{A}$ be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly $\mathscr{A}$-summable if and only if it is $B$-summable for all matrices $B$ of linear…

We prove, using a theorem of Northcott, that if a number field K with s real embeddings and 2t complex ones has a group of units U such that all elements in U have all its complex conjugates of same absolute value, then one necessarily has…

The van Kampen-Flores theorem states that the $n$-skeleton of a $(2n+2)$-simplex does not embed into $\mathbb{R}^{2n}$. We give two proofs for its generalization to a continuous map from a skeleton of a certain regular CW complex (e.g. a…

We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject only to the condition that the irreducible components of…

A theorem of Grove and Searle directly establishes that positive curvature 2d manifolds M with effective circular symmetry group of dimension 8 or less have positive Euler characteristic X(M): the fixed point set N consists of even…

In this paper, the set of all physical theories is represented by a countable collection of consequence operators. It is established that in the Grundlegend Structure, a nonstandard structure, there exists a function S such that for any…

Given a simplicial idempotent augmented endofunctor $F$ on a simplicial combinatorial model category $M$, under the assumption of Vopenka's principle, we exhibit a set $A$ of cofibrant objects in $M$ such that $F$ is equivalent to $\CW_A$,…

We identify a universal short-time structure in symmetry-resolved entanglement dynamics -- the entanglement channel wave (ECW) -- arising from the decomposition of entanglement into conserved-quantum-number sectors that host robust,…

We study regular irreducible inclusions $B\subset A$ of simple unital $C^*$-algebras admitting a conditional expectation. We introduce a generalized notion of quasi-basis extending Watatani's framework and show that such inclusions admit a…

An unusual formula for the Euler characteristics of even dimensional triangulated manifolds is deduced from the generalized Dehn-Sommerville equations.