1,720,973 research outputs found
On directed-convex polyominoes in a rectangle
No full textWe provide bijective proofs for the number of directed-convex polyominoes having a fixed number of rows and columns in two ways: by means of the ECO method, and through a correspondence with the set of 2-colored Grand-Motzkin paths
An algorithm for the reconstruction of discrete sets from two projections in present of absorption
No full textIn this paperweconsider the problem of reconstructing a binary matrix from absorbed projections, as introduced in [Kuba and Nivat, Linear Algebra Appl. 339 (2001) 171–194]. In particular we prove that two left and right horizontal absorbed projections along a single direction uniquely determine a row of a binary matrix for a specific absorption coefficient. Moreover, we give a linear time algorithm which reconstructs such a row and we analyze its performances by determining the worst case complexity.
Finally, we study the same problems in the presence of different absorption coefficients
A combinatorial interpretation of the recurrence f(n+1) = 6f(n) - f(n-1),
No full textWe solve the open problem proposed by Bonin et al. in Journal of Statistical Planning and Inference, 34 (1993) concerning the determination of a combinatorial interpretation of the recursive relation satisfied by NSW numbers. This is done by a bijective proof involving a regular language
A technology for reverse-engineering a combinatorial problem from a rational generating function
No full textIn this paper, we tackle the problem of giving, by means of a regular language, a combinatorial interpretation of a positive sequence (f(n)) defined by a linear recurrence with integer coefficients. We propose two algorithms able to determine if the rational generating function of (f(n)), f(chi), is the generating function of some regular language, and, in the affirmative case, to find it. We illustrate some applications of this method to combinatorial object enumeration problems and bijective combinatorics and discuss an open problem regarding languages having a rational generating function. (C) 2001 Academic Press
Succession rules and deco polyominoes
Full text linkIn this paper, we examine the class of "deco" polyominoes and the succession rule describing their construction. These polyominoes are enumerated according to their directed height by factorial numbers. By changing some aspects of the "factorial" rule, we obtain some succession rules that describe various "deco" polyomino subclasses. By enumerating the subclasses according to their height and width, we find the following well-known numbers: Stirling numbers of the first and second kind, Narayana and odd index Fibonacci numbers. We wish to point out how the changes made on the original succession rule yield some new succession rules that produce transcendental, algebraic and rational generating functions
Reconstruction of Discrete Sets from Three or More X-Rays
No full textThe problem of reconstructing a discrete set from its X-rays in a finite number of prescribed directions is NP-complete when the number of prescribed directions is greater than two. In this paper, we consider an interesting subclass of discrete sets having some connectivity and convexity properties and we provide a polynomial-time algorithm for reconstructing a discrete set of this class from its X-rays in directions (1, 0), (0, 1) and (1, 1). This algorithm can be easily extended to contexts having more than three X-rays
Reconstruction of lattice sets from their horizontal, vertical and diagonal X-rays
No full textIn this paper, we study the problem of reconstructing a lattice set from its X-rays in a finite number of prescribed directions. The problem is NP-complete when the number of prescribed directions is greater than two. We provide a polynomial-time algorithm for reconstructing an interesting subclass of lattice sets (having some connectivity properties) from its X-rays in directions (1,0), (0,1) and (1,1). This algorithm can be easily extended to contexts having more than three X-rays
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
- …
