In this article, we study two open problems posed by Edelman & Reiner about topology of certain simplicial complexes associated with abstract convex geometries. As a special case, we concentrate on generalized convex shellings, which were introduced by Kashiwabara, Nakamura & Okamoto for their representation theorem of abstract convex geometries. We answer one of the problems affirmatively for ...

The classical ring of integer-valued polynomials Int(Z) consists of the polynomials in Q[X] that map Z into Z. We consider a generalization of integervalued polynomials where elements of Q[X] act on sets such as rings of algebraic integers or the ring of n× n matrices with entries in Z. The collection of polynomials thus produced is a subring of Int(Z), and the principal question we consider is...

Problem, research strategy, and findings The 1968 Fair Housing Act required local government recipients of federal money to take meaningful actions affirmatively further fair housing (AFFH). Current analysis requirements are copious but do not request an assessment how land use policies affect the potential for neighborhood integration. A recent California law requires governments include AFFH ...

Let S be a numerical semigroup with embedding dimension e(S), Frobenius number g(S), and type t(S). Put n(S) := Card(S ∩ {0, 1, . . . , g(S)}). A question of Wilf is shown to be equivalent to the statement that e(S)n(S) ≥ g(S)+1. This question is answered affirmatively if S is symmetric, pseudo-symmetric, or of maximal embedding dimension. The question is also answered affirmatively in the foll...

the problem of pleasure is one of the long life, great, effective and much as disputable during the human history. and a variety of philosophical-ethical schools, and also religions, divine and non-divine have paid attention - affirmatively or negatively - to it since a long time ago. although, avicenna has been affected in his definition of the pleasure by scholars of the past, but he had not ...

Abstract How is philosophical knowledge related to the world in which it produced – and how should be related? In article, “world” refers whole of historically established, politically contested materially constituted practices. Three ideal-type relationships are distinguished: affirmatively , negatively against with . The article argues for latter because combines two decisive insights first r...

In an attempt to question the ascendency of today’s relativism, this essay asks two different but interrelated questions: (1) Does the celebration of cultural differences guarantee the disappearance of ethnocentric universalism? (2) Is it possible to envision a universalism that is not ethnocentric? Answering the first question negatively and the second question affirmatively, this essay analyz...