Related papers: Towards a Splitter Theorem for Internally $4$-conn…

We give necessary and sufficient conditions for a closed smooth 6-manifold N to be diffeomorphic to a product of a surface F and a simply connected 4-manifold M in terms of basic invariants like the fundamental group and cohomological data.…

The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…

Splitting operation in Matroid Theory does not preserve graphicness, connectedness, cographicness, etc. Also, the splitting of binary gammoid does not necessarily be binary gammoid after splitting. We have characterized a class of graphic…

Let $M$ be a matroid defined on a finite set $E$ and $L\subset E$. $L$ is locked in $M$ if $M|L$ and $M^*|(E\backslash L)$ are 2-connected, and $min\{r(L), r^*(E\backslash L)\} \geq 2$. Locked subsets characterize nontrivial facets of the…

An input pair $(A,B)$ is triangular input normal if and only if $A$ is triangular and $AA^* + BB^* = I_n$, where $I_n$ is theidentity matrix. Input normal pairs generate an orthonormal basis for the impulse response. Every input pair may be…

We classify the holomorphic structures of the tangent vertical bundle T of the twistor fibration of a quaternionic manifold (M,Q) of dimension bigger than four. In particular, we show that any self-dual quaternionic connection on (M, Q)…

We characterise the following property by six obstructions: given a graphic matroid $M$ and a set $X$ of its elements, when is $M$ the cycle matroid of a graph $G$ such that $X$ is a connected edge set in $G$?

If $\mathcal{C}$ is a minor-closed class of matroids, the class $\mathcal{C}'$ of integer polymatroids whose natural matroids are in $\mathcal{C}$ is also minor closed, as is the class $\mathcal{C}'_k$ of $k$-polymatroids in $\mathcal{C}'$.…

We show that there exist split, orientable, 2-component surface-links in $S^4$ with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m,n$ with $m\ge 4$, the unlink $L_{m,n}$ consisting of one…

If and only if the small neutrino mixing sine s_13 is put zero, the effective neutrino mass matrix M with any mixing sines s_12 and s_23 is invariant under a cyclic group Z_2 of the order two and -- in the limit of m_2 - m_1 --> 0 -- also…

We provide non-trivial checks of $\mathcal{N}=4, D=3$ mirror symmetry in a large class of quiver gauge theories whose Type IIB (Hanany-Witten) descriptions involve D3 branes ending on orbifold/orientifold 5-planes at the boundary. From the…

A positroid is an ordered matroid realizable by a real matrix with all nonnegative maximal minors. Postnikov gave a map from ordered matroids to Grassmann necklaces, for which there is a unique positroid in each fiber of the map. Here, we…

Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of the gauge invariant couplings at order $\ell_p^6$ for the bosonic fields of M-theory, we have found that the minimum number…

We consider M theory 5-branes with compact transverse dimensions. In certain limits the theory on the 5-brane decouples and defines ``little string theories'' in 5+1 dimensions. We show that the familiar structure of IIA/IIB,M,F- theory in…

In this paper, we define the notion of rigidity for linear electrical multiports and for matroid pairs. We show the parallel between the two and study the consequences of this parallel. We present applications to testing, using purely…

Although much progress has been made on the physics of magic angle twisted bilayer graphene at integer fillings, little attention has been given to fractional fillings. Here we show that the three-peak structure of Wannier orbitals,…

We provide a complete structural characterization of $K_{2,4}$-minor-free graphs. The $3$-connected $K_{2,4}$-minor-free graphs consist of nine small graphs on at most eight vertices, together with a family of planar graphs that contains…

For planar graphs, it is well known that high connectivity implies a Hamiltonian cycle and hence any 4-connected planar graph has a near-perfect matching. Nevertheless, whether 6-connected 1-planar graphs admit near-perfect matchings…

Let $(R, \mathfrak{m})$ be a noetherian local ring, $M$ a separated $R$-module (i.e. $\bigcap\limits_{n\geq 1}\mathfrak{m}^n M = 0$) and $\widehat{M} = \lim\limits_{\leftarrow} M/\mathfrak{m}^n M$ its completion. Generally, $M$ is not pure…

There are many results asserting the existence of tree-decompositions of minimal width which still represent local connectivity properties of the underlying graph, perhaps the best-known being Thomas' theorem that proves for every graph $G$…