1,721,035 research outputs found
MIN-turns and MAX-turns in k-Dyck paths: a pure generating function approach
Get PDF-Dyck paths differ from ordinary Dyck paths by using an up-step of length
. We analyze at which level the path is after the -th up-step and before
the st up-step. In honour of Rainer Kemp who studied a related concept
40 years ago the terms \textsc{max}-terms and \textsc{min}-terms are used.
Results are obtained by an appropriate use of trivariate generating functions;
practically no combinatorial arguments are used
Distribution of peak heights modulo and double descents on -Dyck paths
Get PDFWe show that the distribution of the number of peaks at height modulo
in -Dyck paths of a given length is independent of and is the
reversal of the distribution of the total number of peaks. Moreover, these
statistics, together with the number of double descents, are jointly
equidistributed with any of their permutations. We also generalize this result
to generalized Motzkin paths and generalized ballot paths.Comment: 11 pages, 3 figure
MIN-turns and MAX-turns in k-Dyck paths: A pure generating function approach
Get PDFk-Dyck paths differ from ordinary Dyck paths by using an up-step of length k. We analyze at which level the path is after the s-th up-step and before the (s+1)-st up-step. In honour of Rainer Kemp who studied a related concept 40 years ago the terms MAX-terms and MIN-terms are used. Results are obtained by an appropriate use of trivariate generating functions; practically no combinatorial arguments are used
On a generalisation of k-Dyck paths
Get PDFThesis (MSc)--Stellenbosch University, 2019.ENGLISH ABSTRACT: (Refer to full text abstract for symbols that did not transfer correctly). We consider a family of non-negative lattice paths consisting of the step set f(1; 1); (1;k)g called k-Dyck paths, which are enumerated by the generalised Catalan numbers 1 (k+1)n+1 (k+1)n+1
n . By removing the non-negativity condition but restricting the path to stay above the line y = t we obtain a family of lattice paths called kt-Dyck paths which are enumerated by `generalised generalised Catalan numbers
t + 1 (k + 1)n + t + 1 (k + 1)n + t + 1 n : We provide proofs of the enumeration of these paths by means of a bijection, the kernel method, the cycle lemma, and the symbolic method. Analysis of parameters associated with the paths is also performed using symbolic equations
{ particularly the number of peaks, the number of valleys, and the number of returns. These kt-Dyck paths nd application in enumerating a family of walks in the quarter plane (Z 0 Z 0) with step set f(1; 1); (1;k +1); (k; 0)g. Such walks can be decomposed into ordered pairs of kt-Dyck paths and thus their enumeration can be proved via a simple bijection. Through this bijection some parameters in kt-Dyck paths are preserved. Finally, we discuss two different families of lattice paths, S-Motzkin and T-
Motzkin paths, which are related to kt-Dyck paths when k = 2 along with t = 0 and t = 1. We provide bijections between these paths and other combinatorial objects, and perform analysis of parameters in these paths.AFRIKAANSE OPSOMMING: (Verwys na volteks opsomming vir simbole wat nie korrek oorgeskryf het nie). Ons beskou 'n familie van nie-negatiewe roosterpaaie wat bestaan uit die stap-
versameling f(1; 1); (1;k)g genoem k-Dyck paaie, wat deur die veralgemeende
Catalan getalle, 1
(k+1)n+1
(k+1)n+1
n
, getel word. Deur die nie-negatiwiteitsvereiste
te verwyder, maar die pad tot bokant die lyn y = t te beperk kry ons 'n fami-
lie roosterpaaie genaamd kt-Dyck paaie wat getel word deur `veralgemeende'
veralgemeende Catalan getalle
t + 1
(k + 1)n + t + 1
(k + 1)n + t + 1
n
:
Ons lewer 'n bewys van die aftelling van hierdie paaie deur middel van 'n
bijeksie, die kernmetode, die sikluslemma en die simboliese metode. Analise
van parameters wat met die paaie geassosieer word, word ook uitgevoer met
behulp van simboliese vergelykings { veral die aantal pieke, die aantal valleie
en die aantal terugkomste.
Hierdie kt-Dyck paaie vind 'n toepassing in 'n familie van wandelinge in
die kwartvlak (Z 0 Z 0) met stapversameling f(1; 1); (1;k + 1); (k; 0)g.
Sulke wandelinge kan ontleed word in geordende pare kt-Dyck paaie en dus
kan hul aftelling deur middel van 'n eenvoudige bijeksie bewys word. Deur
hierdie bijeksie word 'n paar parameters in kt-Dyck paaie bewaar.
Laastens bespreek ons twee verskillende families van roosterpaaie, S-Motzkin
en T-Motzkin paaie, wat verband hou met kt-Dyck paaie wanneer k = 2 saam
met t = 0 en t = 1. Ons bied bijeksies tussen hierdie paaie en ander kom-
binatoriese voorwerpe, en doen 'n analise van parameters op hierdie paaie.Master
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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