Related papers: A binary invariant of matrix mutation
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.
For a wide class of pairs of unbounded selfadjoint operators with bounded commutator we construct a K-theoretical integer invariant which is continuous, is equal to zero for commuting operators and is equal to one for the pair (x, i d/dx).
Algebraic statistics for binary random variables is concerned with highly structured algebraic varieties in the space of 2x2x...x2-tensors. We demonstrate the advantages of representing such varieties in the coordinate system of binary…
"An invariant of metric spaces under bornologous equivalences" gives an invariant and "A coarse invariant" extends the invariant to coarse equivalences. In both papers the invariant is defined for a class of metric spaces called sigma…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…
We study $n$-dimensional matrices with $\{0,1\}$-entries ($n$-cubes) such that all their $2$-dimensional slices are incidence matrices of symmetric designs. A known construction of these objects obtained from difference sets is generalized…
This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
We consider Open Gromov-Witten invariants for noncompact Calabi-Yau in the case the Lagrangian has the topology of $\R^2 \times S^1$. The definition of the invariant involves the choice of a frame for the Lagrangian, in accord with string…
We consider the alternating sign matrices of the odd order that have some kind of central symmetry. Namely, we deal with matrices invariant under the half-turn, quarter-turn and flips in both diagonals. In all these cases, there are two…
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…
We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the…
We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both…
We introduce invariant algebras and representation$^{(c_1,..., c_8)}$ of algebras, and give many ways of constructing Lie algebras, Jordan algebras, Leibniz algebras, pre-Lie algebras and left-symmetric algebras in an invariant algebras.
We construct a neutrino mass matrix $M_{\nu}$ via a seesaw mechanism whith perturbed invariant under a cyclic permutation by introducing one parameter $\delta$ into the diagonal elements of $M_{\nu}$ with assumption that trace of the…
Under binary matrices we mean matrices whose entries take one of two values. In this paper, explicit formulae for calculating the determinant of some type of binary Toeplitz matrices are obtained. Examples of the application of the…