Two words have a reverse if they have the same pair of distinct letters on the same pair of positions, but in reversed order. A set of words no two of which have a reverse is said to be reverse-free. Let F (n, k) be the maximum size of a reversefree set of words from [n]k where no letter repeats within a word. We show the following lower and upper bounds in the case n ≥ k: F (n, k) ∈ nkk−k/2+O(...

In what case do you like reading so much? What about the type of the scale free networks complex webs in nature and technology book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining books become so popu...

We define a new combinatorial object, which we call a labeled hypergraph, uniquely associated to any square-free monomial ideal. We prove several upper bounds on the regularity of a square-free monomial ideal in terms of simple combinatorial properties of its labeled hypergraph. We also give specific formulas for the regularity of square-free monomial ideals with certain labeled hypergraphs. Fu...

This paper presents a novel approach for generating Context-Free Grammars (CFGs) from small sets of input strings (a single input string in some cases). Our approach is to compile this task into a classical planning problem whose solutions are sequences of actions that build and validate a CFG compliant with the input strings. In addition, we show that our compilation is suitable for implementi...

In this paper we introduce a new setting, based on partial algebras, for studying constructions of finitely generated free algebras. We give sufficient conditions under which the finitely generated free algebras for a variety V may be described as the colimit of a chain of finite partial algebras obtained by repeated application of a functor. In particular, our method encompasses the constructi...

If one converts surface lters into context free rules, one has to introduce new features. These features are strictly nonlexical, and their distribution is predictable from the distribution of the lexical features. Now, given a (feature based) context free grammar, we ask whether one can identify the nonlexical features. This is not possible; however, the notion of an inessential feature ooers ...

Thue [14] showed that there exist arbitrarily long square-free strings over an alphabet of three symbols (not true for two symbols). An open problem was posed in [7], which is a generalization of Thue’s original result: given an alphabet list L = L1, . . . , Ln, where |Li| = 3, is it always possible to find a square-free string, w = w1w2 . . .wn, where wi ∈ Li? In this paper we show that square...

This paper develops a new framework to examine the use of ‘evaluation resources’ in research discourse. In previous studies of evaluative resources, two distinct, although interwoven, types of context have been identified: 1) the real world where evaluation resources are used to describe situations, and 2) the research world studying the real world, where they are used to engage readers and ope...

This article concerns a free boundary problem for a reactiondiffusion system modeling the cooperative interaction of two diffusion biological species in one space dimension. First we show the existence and uniqueness of a local classical solution, then we study the asymptotic behavior of the free boundary problem. Our results show that the free boundary problem admits a global solution if the i...

We show how contextual hyperedge replacement grammars can be used to generate abstract meaning representations (AMRs), and argue that they are more suitable for this purpose than hyperedge replacement grammars. Contextual hyperedge replacement turns out to have two advantages over plain hyperedge replacement: it can completely cover the language of all AMRs over a given domain of concepts, and ...