Considered is the multiplicative semigroup of ratios of products of principal minors bounded over all positive definite matrices. A long history of literature identifies various elements of this semigroup, all of which lie in a subsemigroup generated by Hadamard-Fischer inequalities. Via cone-theoretic techniques and the patterns of nullity among positive semidefinite matrices, a semigroup cont...

We prove refined enumeration results on several symmetry classes as well related of alternating sign matrices with respect to classical boundary statistics, using the six-vertex model statistical physics. More precisely, we study vertically symmetric, and horizontally perverse, off-diagonally off-antidiagonally quarter turn symmetric quasi matrices. Our conjectures Fischer, Duchon Robbins.

In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...

Abstract A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix height ${\mathfrak h}$ , where the distributivity number ${\cal P} (\omega ) / {\mathrm {fin}}$ . We show if continuum c}$ regular, then are matrices any regular uncountable $\leq {\mathfrak in Cohen random models. This answers questions Fischer, Koelbing, Wohofsky.

The orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups the form 36:L4(3). These groups are all isomorphic to each other and order 4421589120 with index 1120 in (3). In this paper, we will compute ordinary carácter table one these using technique Fischer-Clifford matrices. This is very efficient character an extension Ḡ = N.G especially where normal subgroup N element...

The class of normal subshifts includes irreducible nontrivial topological Markov shifts, sofic synchronized systems, Dyck β-shifts, substitution minimal and so on. We will characterize one-sided conjugacy classes in terms the associated C∗-algebras its gauge actions with potentials. In particular, shifts are characterized simple purely infinite Cuntz-Krieger algebras matrices left Fischer cover...