Koh and Tan gave a sufficient condition for a 3-partite tournament to have at least one 3-king in [K.M. Koh, B.P. Tan, Kings in multipartite tournaments, Discrete Math. 147 (1995) 171–183, Theorem 2]. In Theorem 1 of this paper, we extend this result to n-partite tournaments, where n 3. In [K.M. Koh, B.P. Tan, Number of 4-kings in bipartite tournaments with no 3-kings, Discrete Math. 154 (1996)...

From the perspective of structural linguistics, we explore paradigmatic and syntagmatic lexical relations for Chinese POS tagging, an important and challenging task for Chinese language processing. Paradigmatic lexical relations are explicitly captured by word clustering on large-scale unlabeled data and are used to design new features to enhance a discriminative tagger. Syntagmatic lexical rel...

We show that in any n-partite tournament, where n/> 3, with no transmitters and no 3-kings, the number of 4-kings is at least eight. All n-partite tournaments, where n/>3, having eight 4-kings and no 3-kings are completely characterized. This solves the problem proposed in Koh and Tan (accepted).

Traditionally, syntagmatic processes refer to the influence of “horizontal” elements on a word or phrase, in contradistinction to paradigmatic processes, which refer to “vertical” or alternative substitutions in a phrase. The term had significant currency in early and mid-twentieth century linguistics from Saussure on, and helped to define the formal study of syntax as widely practiced today. T...

A tournament Tn is an orientation of a complete graph on n vertices. A king in a tournament is a vertex from which every other vertex is reachable by a path of length at most 2. A sorted sequence of kings in a tournament Tn is an ordered list of its vertices u1, u2, . . . , un such that ui dominates ui+1 (ui → ui+1) and ui is a king in the subtournament induced by {uj : i ≤ j ≤ n} for each i = ...