1,720,979 research outputs found
Ascending runs in permutations and valued Dyck paths
No full textAbstract
We define a bijection between permutations and valued Dyck paths, namely, Dyck
paths whose odd vertices are labelled with an integer that does not exceed their height.
This map allows us to characterize the set of permutations avoiding the pattern 132 as
the preimage of the set of Dyck paths with minimal labeling. Moreover, exploiting this
bijection we associate to the set of n-permutations a polynomial that generalizes at the
same time Eulerian polynomials, Motzkin numbers, super-Catalan numbers, little Schr ̈oder
numbers, and other combinatorial sequences. Lastly, we determine the Hankel transform
of the sequence of such polynomials
Permutations Avoiding a Simsun Pattern
Full text linkA permutation π avoids the simsun pattern τ if π avoids the consecutive pattern τ and the same condition applies to the restriction of π to any interval [k]. Permutations avoiding the simsun pattern 321 are the usual simsun permutation introduced by Simion and Sundaram. Deutsch and Elizalde enumerated the set of simsun permutations that avoid in addition any set of patterns of length 3 in the classical sense. In this paper we enumerate the set of permutations avoiding any other simsun pattern of length 3 together with any set of classical patterns of length 3.
The main tool in the proofs is a massive use of a bijection between permutations and increasing binary trees
Pattern avoiding alternating involutions
Full text linkWe enumerate and characterize some classes of alternating and reverse
alternating involutions avoiding a single pattern of length three or four. If
on one hand the case of patterns of length three is trivial, on the other hand,
the length four case is more challenging and involves sequences of
combinatorial interest, such as Motzkin and Fibonacci numbers
Two descent statistics over 321-avoiding centrosymmetric involutions
Full text linkCentrosymmetric involutions in the symmetric group S_{2n} are permutations pi such that pi = pi^{- 1} and pi(i)+ pi(2n + 1 - i) = 2n + 1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the distribu- tion of some natural descent statistics on 321-avoiding centrosymmetric involutions, including the number of descents in the rst half of the involution, and the sum of the positions of these descents. Our results are based on two new bijections, one between centrosymmetric involutions in S_{2n} and subsets of {1; ...; n}, and another one showing that certain statistics on Young diagrams that fit inside a rectangle are equidistributed. We also use the latter bijection to rene a known result stating that the distribution of the major index on 321-avoiding involutions is given by the q-analogue of the central binomial coefficients
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
Giochi Matematici come strumento didattico
Full text linkIn questa tesi e' stato fatto un lavoro prima creativo e poi pratico di tipologia didattica. Prima di tutto sono avvenuti degli incontri a Parma nei quali ho imparato a scrivere i giochi matematici confrontandomi con degli esperti. A questo lavoro e' seguitala creazione di una prova a cui sottoporre degli studenti delle medie. E con le conoscenze ottenute dagli incontri ho creato un compito composto da 7 esercizi con lo scopo di valutare ma soprattutto stimolare ogni parte del ragionamento matematico in un ragazzo. A questo lavoro e' seguito quello in classe dove sono stati dati i compiti e poi e' stata fatta la correzione insieme alle classi e infine la raccolta dati e il commento. Con anche l’aiuto delle insegnanti che mi hanno coinvolto nell’attivita' sia durante l’attivita' didattica che successivamente fornendo il quadro completo della classe. La tesi e' strutturata in tre parti: nel primo capitolo farò un’introduzione storica e filosofica sulla matematica e in particolare sui giochi matematici nelle scuole, spiegando nel dettaglio che cosa mi ha portato a svolgere questo lavoro. Nel secondo capitolo invece parlerò del compito stesso, di come e' stato concepito con particolare attenzione nei singoli quesiti. Infine nel terzo discuterò dei risultati ottenuti dagli studenti, guardando le percentuali di esercizi corretti e dedicando l’ultima sezione agli errori piu' comuni
Semistandard tableaux associated with generalized labellings of posets
No full textAbstractWe describe a correspondence between a family of labelled partially ordered sets and semistandard Young tableaux. Moreover, we define some operations among labelled posets which naturally correspond to operations among the associated semistandard Young tableaux
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
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