1,720,960 research outputs found
A cycle lemma for permutation inversions
No full textIn this paper we study some properties of the inversion statistic. Some enumerative results concerning the permutations of the multiset {xm1 ; xm2} with respect to the inversion parameter
are established and it is shown that these depend on gcd(m1; m2). Using a “cycle lemma”, a combinatorial proof of the results is given. Moreover, some applications to the Gaussian binomial
coe4cient are illustrated
An equipartition property for the distribution of multiset permutation inversions
No full textThe purpose of this paper is to present some enumerative results concerning the class View the MathML sourcek of permutations of the multiset {1m1, 2m2,...,rmr} having inversion number congruent to k modulo n, with n = m1 + m2 + ··· + mr and 0 ≤ k < n. We show that the enumeration of this family of permutations is connected to gcd(m1, m2,...,mr), and if gcd(m1, m2,...,mr) = 1, then View the MathML source, for each 0 ≤ k < n. Finally, some applications of these properties concerning the q-multinomial coefficient are found
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
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
A general cyclic lemma for multiset permutation inversions
No full textWe present some enumerative results concerning the permutations of the multiset {x_1^{m_1},...,x_r^{m_r}} having inversion number congruent to k modulo n,
Reconstruction of 4- and 8-connected convex discrete sets from row and column projections
No full textIn this paper we examine the problem of reconstructing a discrete two-dimensional set from its two orthogonal projection (H,V) when the set satisfies some convexity conditions. We show that the algorithm of the paper [Int. J. Imaging Systems and Technol. 9 (1998) 69] is a good heuristic algorithm but it does not solve the problem for all (H,V) instances. We propose a modification of this algorithm solving the problem for all (H,V) instances, by starting to build the "spine". The complexity of our reconstruction algorithm is O(mn·log(mn)·min{m2,n2}) in the worst case. However, according to our experimental results, in 99% of the studied cases the algorithm is able to reconstruct a solution without using the newly introduced operation. In such cases the upper bound of the complexity of the algorithm is O(mn·log(mn)). A systematic comparison of this algorithm was done and the results show that this algorithm has the better average complexity than other published algorithms. The way of comparison and the results are given in a separate paper [Linear Algebra Appl. (submitted)]. Finally we prove that the problem can be solved in polynomial time also in a class of discrete sets which is larger than the class of convex polyominoes, namely, in the class of 8-connected convex set
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
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