Advances in Discrete Applied Mathematics and Graph Theory

The present reprint contains twelve papers published in the Special Issue “Advances in Discrete Applied Mathematics and Graph Theory, 2021” of the MDPI Mathematics journal, which cover a wide range of topics connected to the theory and applications of Graph Theory and Discrete Applied Mathematics. The focus of the majority of papers is on recent advances in graph theory and applications in chemical graph theory. In particular, the topics studied include bipartite and multipartite Ramsey numbers, graph coloring and chromatic numbers, several varieties of domination (Double Roman, Quasi-Total Roman, Total 3-Roman) and two graph indices of interest in chemical graph theory (Sombor index, generalized ABC index), as well as hyperspaces of graphs and local inclusive distance vertex irregular graphs

Commodity Taxation and Social Welfare: The Generalised Ramsey Rule

Commodity taxes have three distinct roles: (1) revenue collection, (2) interpersonal redistribution, and (3) resource allocation. The paper presents an integrated treatment of these three concerns in a second-best general equilibrium framework, which leads to the "generalised Ramsey rule for optimum taxation. We show how many standard results on optimum taxation and tax reform have straightforward counterpart in this general framework. Using this framework, we also try to clarify the notion of "deadweight loss", as well as the relation between alternative distributional assumptions and the structure of optimum taxes.

Commodity Taxation and Social Welfare: The Generalised Ramsey Rule

Commodity taxes have three distinct roles: (1) revenue collection, (2) interpersonal redistribution, and (3) resource allocation. The paper presents an integrated treatment of these three concerns in a second-best general equilibrium framework, which leads to the 'generalised Ramsey rule' for optimum taxation. We show how many standard results on optimum taxation and tax reform have a straightforward counterpart in this general framework. Using this framework, we also try to clarify the notion of 'deadweight loss' as well as the relation between alternative distributional assumptions and the structure of optimum taxes.Commodity taxation, efficiency, redistribution, shadow prices

Alien Structure and Themes from Analytic Philosophy

We think of the world as consisting of objects, with properties and standing in relations. There are, to be sure, different views on what objects etc. there are, and on what their natures are. And some theorists want to subtract some elements from this picture. For example, the ontological nihilist says that there are no objects. But still, the view described is very much orthodoxy—so much orthodoxy that one may need to be reminded that the view that the world consists of objects, with properties and standing in relations is, precisely, a view. I here investigate the possibility that this view is false: that there is what may be called alien structure. And I investigate the relationship between alien structure and some important themes from the history of analytic philosophy