1,720,960 research outputs found
Primitive elements of the Hopf algebras of tableaux
Full text linkThe character theory of symmetric groups, and the theory of symmetric functions, both make use of the combinatorics of Young tableaux, such as the Robinson–Schensted algorithm, Schützenberger's “jeu de taquin”, and evacuation. In 1995 Poirier and the second author introduced some algebraic structures, different from the plactic monoid, which induce some products and coproducts of tableaux, with homomorphisms. Their starting point are the two dual Hopf algebras of permutations, introduced by the authors in 1995. In 2006 Aguiar and Sottile studied in more detail the Hopf algebra of permutations: among other things, they introduce a new basis, by Möbius inversion in the poset of weak order, that allows them to describe the primitive elements of the Hopf algebra of permutations. In the present Note, by a similar method, we determine the primitive elements of the Poirier–Reutenauer algebra of tableaux, using a partial order on tableaux defined by Taskin
The Fortuin–Kasteleyn polynomial as a bialgebra morphism and applications to the Tutte polynomial
No full textWe compute an explicit formula for the antipode of the double bialgebra of graphs in terms of totally acyclic partial orientations, using some general results on double bialgebras. In analogy to what was already proven in Hopf-algebraic terms for the chromatic polynomial of a graph, we show that the Fortuin–Kasteleyn polynomial (a variant of the Tutte polynomial) is a morphism of the double algebra of graphs into that of polynomials, which generalizes the chromatic polynomial. When specialized at particular values, we give combinatorial interpretations of the Tutte polynomial of a graph, via covering graphs and covering forests, and of the Fortuin–Kasteleyn polynomial, via pairs of vertex-edge colorings. Finally we show that the map associating to a graph all its orientations is a Hopf morphism from the double bialgebra of graphs into the one of oriented graphs, allowing to give interpretations of the Fortuin–Kasteleyn polynomial when computed at negative values. © The copyright of this article is retained by the Author(s)
Enumerating permutation polynomials. II. -cycles with minimal degree
No full textAbstractWe consider the function m[k](q) that counts the number of cycle permutations of a finite field Fq of fixed length k such that their permutation polynomial has the smallest possible degree. We prove the upper-bound m[k](q)⩽(k−1)!(q(q−1))/k for char(Fq)>e(k−3)/e and the lower-bound m[k](q)⩾ϕ(k)(q(q−1))/k for q≡1(modk). This is done by establishing a connection with the Fq-solutions of a system of equations Ak defined over Z. As example, we give complete formulas for m[k](q) when k=4,5 and partial formulas for k=6. Finally, we analyze the Galois structure of the algebraic set Ak
Symmetril Moulds, Generic Group Schemes, Resummation of MZVs
No full textThe present article deals with various generating series and group schemes (not necessarily affine ones) associated with MZVs. Our developments are motivated by Ecalle’s mould calculus approach to the latter. We propose in particular a Hopf algebra–type encoding of symmetril moulds and introduce a new resummation process for MZVs
Corrigendum to: "Enumerating permutation polynomials. I. Permutations with non-maximal degree"
No full textIt corrects a paper appeared in
Finite Fields Appl. 8 (2002) 531–54
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
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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