This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using...

We study a model in which voters choose between two candidates on the basis of both ideology and competence. While the ideology of the candidates is commonly known, voters are imperfectly informed about competence. Voter preferences, however, are such that it is a dominant strategy to vote according to ideology alone. When voting is compulsory, the candidate of the majority ideology prevails an...

We prove that a universal preference type space exists under much more general conditions than those postulated by Epstein and Wang (1996). To wit, it is enough that preferences can be encoded by a countable collection of continuous functionals, while the preferences themselves need not necessarily be continuous or regular, like, e.g., in the case of lexicographic preferences. The proof relies ...

A lexicographic integer optimization problem with criteria represented by absolute values of linear functions is considered. Five types of stability for the set of lexicographic optima under small changes of the parameters of the vector criterion are investigated.

Sets of lexicographic probabilities and sets of desirable gambles share several features, despite their apparent differences. In this paper we examine properties of marginalization, conditioning and independence for sets of lexicographic probabilities and sets of desirable gambles.

The lexicographic flow problem is a flow problem in which the edges are assigned priorities, and we wish to find a flow that is lexicographically maximum with respect to the priority assignment. The problem is reducible to a weighted flow problem, but we show that exponentially large weights are necessary in general. We then give an efficient direct algorithm that does not use weights.

Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. The polyranking principle is proposed as a generalization of polynomial ranking for analyzing termination of loops. We define lexicographic polyranking functions in the context of loops with parallel transitions ...

The Hall-ratio ρ(G) of a graph G is the ratio of the number of vertices and the independence number maximized over all subgraphs of G. The ultimate lexicographic Hall-ratio of a graph G is defined as limn→∞ n √ ρ(G◦n), where G◦n denotes the nth lexicographic power of G (that is, n times repeated substitution of G into itself). Here we prove the conjecture of Simonyi stating that the ultimate le...