In this paper we discuss the development of a multilingual collocation dictionary for translation purposes. By ‘collocation’ we mean not only set or fixed expressions including idioms, simple cooccurrences of items and metaphorical uses, but also translators’ paraphrases. We approach this problem from two directions. Firstly we identify certain linguistic phenomena and lexicographical requireme...

Nowadays, many strategies to solve polynomial systems use the computation of a Gröbner basis for the graded reverse lexicographical ordering, followed by a change of ordering algorithm to obtain a Gröbner basis for the lexicographical ordering. The change of ordering algorithm is crucial for these strategies. We study the p-adic stability of the main change of ordering algorithm, FGLM. We show ...

Compared with printed dictionaries, online dictionaries provide a number of unique possibilities for the presentation and processing of lexicographical information. However, in Müller-Spitzer/Koplenig/Töpel (2011) we show that – on average users tend to rate the special characteristics of online dictionaries (e.g. multimedia, adaptability) as (partly) unimportant. This result conflicts somewhat...

We give eecient algorithms for listing equivalence classes of k-ary strings under reversal and permutation of alphabet symbols. As representative of each equivalence class we choose that string which is lexicographically smallest. These algorithms use space O(n) and time O(p kN), where N is the total number of strings generated and n is the length of each string. For k = 2, we obtain a recursiv...

When a bibliography is built by extracting references from a data base—as BibTEX does when it builds a bibliography for a LATEX document—these references are usually sorted w.r.t. author names. Nevertheless, most of implementations of lexical order relations on person names consist of concatenations of the parts of names: first name, particle, last name. We show that this may lead to incorrect ...

We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite field can be computed in quasi-linear expected time, using randomized algorithm Las Vegas type. A similar complexity bound is proved for computation lexicographical Gröbner basis ideal generated by polynomials.

In this paper we investigate properties of a certain equivalence relation on reduced words in S, called Ca-equivalence. We combinatorially characterize the class of the lexicographically first reduced word of a permutation. We further show how this class is related to reduced words that are lattice words.

In this paper, we characterize by lexicographic order all finite Sturmian and episturmian words, i.e., all (finite) factors of such infinite words. Consequently, we obtain a characterization of infinite episturmian words in a wide sense (episturmian and episkew infinite words). That is, we characterize the set of all infinite words whose factors are (finite) episturmian. Similarly, we character...

We show that every additively representable comparative probability ordering is determined by at least n− 1 binary subset comparisons. We show that there are many orderings of this kind, not just the lexicographic ordering. These results provide answers to two questions asked by Fishburn.