منابع مشابه
Symmetric alternating sign matrices
In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...
متن کاملEla Spectral Properties of Sign Symmetric Matrices
Spectral properties of sign symmetric matrices are studied. A criterion for sign symmetry of shifted basic circulant permutation matrices is proven, and is then used to answer the question which complex numbers can serve as eigenvalues of sign symmetric 3 × 3 matrices. The results are applied in the discussion of the eigenvalues of QM -matrices. In particular, it is shown that for every positiv...
متن کاملTotally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices
We present multiresidue integral formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 Uq(ŝl2) quantum Knizhnik–Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco ’06] connecting the above to generating polynomials for weighted Totally Symmetric Self-Complem...
متن کاملDiagonally and Antidiagonally Symmetric Alternating Sign Matrices of Odd Order
We study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order by introducing a case of the six-vertex model whose configurations are in bijection with such matrices. The model involves a grid graph on a triangle, with bulk and boundary weights which satisfy the Yang–Baxter and reflection equations. We obtain a general expression for t...
متن کاملOn Weakly Projective Symmetric Manifolds
The object of the present paper is to study weakly projective symmetric manifolds and its decomposability with several non-trivial examples. Among others it is shown that in a decomposable weakly projective symmetric manifold both the decompositions are weakly Ricci symmetric.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1974
ISSN: 0024-3795
DOI: 10.1016/0024-3795(74)90063-9