Does imply axiom of choice?
Does the endomorphism poset determine whether a finite poset is connected? An issue Duffus raised in 1978
Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that is connected and imply that is connected”, where and are finite nonempty posets. We show that, indeed, under these hypotheses is connected and .
Domino Fibonacci tableaux.
Doubly stochastic matrices and the Bruhat order
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class of doubly stochastic matrices (convex hull of permutation matrices). An alternative description of this partial order is given. We define a class of special faces of induced by permutation matrices,...
Dualität zwischen Kategorien topologischer Räume und Kategorien von K-Verbänden.
Dualities associated to binary operations on .
Duality for Cardinal Algebras.
Duality for Hilbert algebras with supremum: An application
We modify slightly the definition of -partial functions given by Celani and Montangie (2012); these partial functions are the morphisms in the category of -space and this category is the dual category of the category with objects the Hilbert algebras with supremum and morphisms, the algebraic homomorphisms. As an application we show that finite pure Hilbert algebras with supremum are determined by the monoid of their endomorphisms.
Dumont's statistic on words.