RALEIGH'S “ORDERS.”

On orders induced by implications

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

Converse Lagrange Theorem Orders and Supersolvable Orders

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...

Extending Partial Orders to Dense Linear Orders

Tree-visibility Orders Tree-visibility Orders

In this paper we introduce a new class of partially ordered sets, called tree-visibility orders, extending the class of interval orders in a fashion similar to the extension of interval graphs to chordal graphs. This class contains interval orders, duals of generalized interval orders and height one orders. We give a characterization of tree-visibility orders by an innnite family of minimal for...

Term Orders

Let n be an ordinal number, let L be an add-associative right complementable right zeroed unital distributive non empty double loop structure, and let m1, m2 be monomials of n, L. Note that m1 ∗m2 is monomial-like. Let n be an ordinal number, let L be an add-associative right complementable right zeroed distributive non empty double loop structure, and let c1, c2 be constant polynomials of n, L...