Related papers: Seifert matrices of Brunnian links

Let $G_n$ be a simple graph on $V_n=\{v_1,\dots, v_n\}$. The Seidel matrix $S(G_n)$ of $G_n$ is the $n\times n$ matrix whose $(ij)$'th entry, for $i\neq j$ is $-1$ if $v_i\sim v_j$ and $1$ otherwise, and whose diagonal entries are $0$. We…

We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex.…

Recently, it has been observed that the kinematic factor of the disk-level S-matrix element of two RR two-forms and the disk-level S-matrix element of two B-fields on the world volume of D$_3$-brane are compatible with the standard rules of…

An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign…

In this note, we perform Sklyanin's construction of commuting open-chain/boundary transfer matrices to the q-deformed SU(2|2) bulk S-matrix of Beisert and Koroteev and a corresponding boundary S-matrix. This also includes a corresponding…

In this paper, we analyse spectral properties of Seidel matrix (denoted by $S$) of connected threshold graphs. We compute the characteristic polynomial and determinant of Seidel matrix of threshold graphs. We derive formulas for the…

We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this…

We establish necessary and sufficient conditions on simultaneous symplectic spectral decomposition of a family of $2n \times 2n$ real positive semidefinite matrices with symplectic kernels. We also provide a precise algebraic condition on a…

There are many results showing the connection and phenomenon between some low-dimensional manifolds with the profinite completions of their fundamental groups. We focus on some Seifert 4-manifolds about the extent of their profinite…

Let $L$ be one of the finite dimensional Lie algebras $W_n({\bf m}),$ $S_n({\bf m}),$ $ H_n({\bf m})$ of Cartan type over an algebraically closed field of prime characteristic $p>0.$ For an elements $F$ of the symmetrical algebra $S(L)$ we…

We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an…

Let $\mathcal S$ be a semigroup of partial isometries acting on a complex, infinite-dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup $\mathcal T$ generated by $\mathcal…

In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…

This study establishes consistency conditions and a general solution for a coupled system that consists of five two-sided Sylvester-like tensor equations in ten quaternion variables throughout the Einstein tensor product. Certain specific…

In this paper we first give a necessary and sufficient condition for a group $G$ generated by $n$ elements to be a square commutative group and prove $G$ is a square commutative group if and only if $\widehat{G}$ is an abelian group, then…

We give a combinatorial description of sl(n)-fusion coefficients in the case where one partition has at most two columns and establih other properties for this case.

Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient…

We show that applying the Bailey lemma to elliptic hypergeometric integrals on the $A_n$ root system leads to a large web of dualities for $\mathcal{N} = 1$ supersymmetric linear quiver theories. The superconformal index of Seiberg's SQCD…

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to…