منابع مشابه
Conference Matrices and Unimodular Lattices
We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...
متن کاملPrincipally Unimodular Skew-Symmetric Matrices
A square matrix is principally unimodular if every principal submatrix has determinant 0 or 1. Let A be a symmetric (0; 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A 0 is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A 0. This construction is based on the fact that the PU-o...
متن کاملUnimodular Matrices in Banach Algebra Theory
Let A be a ring with 1 and denote by L (resp. R) the set of left (resp. right) invertible elements of A. If A has an involution *, there is a natural bijection between L and R. In general, it seems that there is no such bijection; if A is a Banach algebra, L and R are open subsets of A, and they have the same cardinality. More generally, we prove that the spaces Uk(A") of n X i-left-invertible ...
متن کاملOn the discrepancy of strongly unimodular matrices
A (0, 1) matrix A is strongly unimodular if A is totally unimodular and every matrix obtained from A by setting a nonzero entry to 0 is also totally unimodular. Here we consider the linear discrepancy of strongly unimodular matrices. It was proved by Lováz, et.al. [5] that for any matrix A, lindisc(A) ≤ herdisc(A). (1) When A is the incidence matrix of a set-system, a stronger inequality holds:...
متن کاملTilings from non-Pisot unimodular matrices
Using the unimodular Pisot substitution of the free monoid on d letters, the existence of graph-directed self-similar sets fXigi1⁄41; 2;...; d satisfying the set equation (0.0.1) with the positive measure on the A-invariant contracting plane P is well-known, where A is the incidence matrix of the substitution. Moreover, under some conditions, the set fXigi1⁄41; 2;...; d is the prototile of the ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1977
ISSN: 0012-365X
DOI: 10.1016/0012-365x(77)90114-5