This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.

Monolingual corpora were first thought of as an excellent basis for lexicographical research but, as time went on, research projects extended to various kinds of analysis, from the lexicon, to syntactic patterns to various aspects of text structure. Nowadays the study of the general lexicon covers the analysis of single and multi-word units in context, collocations, lexical groups, lexical 'bun...

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the first m words in L according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorith...

Data reordering techniques are applied to improve the space and time efficiency of storage and query systems in various scientific and commercial applications. Run-length encoding is a prominent approach of compression in many areas, whose performance is significantly enhanced by achieving longer and fewer “runs” through data reordering. In this paper we theoretically study two reordering techn...

We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: Consistently relative to a supercompact, there is a nowhere precipitous normal ideal I on א2 such that player nonempty wins the pressing down game of length א1 on I even if player empty starts. For the proof, we construct a forcing notion to force the following: There is normal, nowhere preci...

Coherence-based approaches are quite popular to reason under inconsistency. Most of them are defined with respect to totally preordered belief bases such as the lexicographic inference which is known to have desirable properties from theoretical, practical and psychological points of view. However, partially preordered belief bases offer much more flexibility to represent efficiently incomplete...