1,720,978 research outputs found
Algebraic Combinatorics
No full textThis is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected
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
Mixed Dimer Configuration Model in Type D Cluster Algebras
Full text linkWe give a combinatorial model for F-polynomials and g-vectors for type D
cluster algebras where the associated quiver is acyclic. Our model utilizes a
combination of dimer configurations and double dimer configurations which we
refer to as mixed dimer configurations. In particular, we give a graph
theoretic recipe that describes which monomials appear in such F-polynomials,
as well as a graph theoretic way to determine the coefficients of each of these
monomials. In addition, we give a weighting on our mixed dimer configuration
model that gives the associated g-vector. To prove this formula, we use a
combinatorial formula due to Thao Tran and provide explicit bijections between
her combinatorial model and our own.Comment: 49 pages, 46 figures, updated to address properties of the poset as
well as draw a direct connection to representation theor
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
Labeled Chip-firing on Binary Trees with Chips
Full text linkWe study labeled chip-firing on binary trees and some of its modifications.
We prove a sorting property of terminal configurations of the process. We also
analyze the endgame moves poset and prove that this poset is a modular lattice.Comment: Updated version to appear in Annals of Combinatoric
Higher cluster categories and QFT dualities
Full text linkWe introduce a unified mathematical framework that elegantly describes minimally supersymmetry gauge theories in even dimensions, ranging from six dimensions to zero dimensions, and their dualities. This approach combines and extends recent developments on graded quivers with potentials, higher Ginzburg algebras, and higher cluster categories (also known as m-cluster categories). Quiver mutations studied in the context of mathematics precisely correspond to the order-(m + 1) dualities of the gauge theories. Our work indicates that these equivalences of quiver gauge theories sit inside an infinite family of such generalized dualities
A new characterization for the m-quasiinvariants of Sn and explicit basis for two row hook shapes
No full textAbstractIn 2002, Feigin and Veselov [M. Feigin, A.P. Veselov, Quasiinvariants of Coxeter groups and m-harmonic polynomials, Int. Math. Res. Not. 10 (2002) 521–545] defined the space of m-quasiinvariants for any Coxeter group, building on earlier work of [O.A. Chalykh, A.P. Veselov, Commutative rings of partial differential operators and Lie algebras, Comm. Math. Phys. 126 (1990) 597–611]. While many properties of those spaces were proven in [P. Etingof, V. Ginzburg, On m-quasi-invariants of a Coxeter group, Mosc. Math. J. 3 (2002) 555–566; M. Feigin, A.P. Veselov, Quasiinvariants of Coxeter groups and m-harmonic polynomials, Int. Math. Res. Not. 10 (2002) 521–545; G. Felder, A.P. Veselov, Action of Coxeter groups on m-harmonic polynomials and Knizhnik–Zamolodchikov equations, Mosc. Math. J. 4 (2003) 1269–1291; A. Garsia, N. Wallach, The non-degeneracy of the bilinear form of m-quasi-invariants, Adv. in Appl. Math. 3 (2006) 309–359. [7]] from this definition, an explicit computation of a basis was only done in certain cases. In particular, in [M. Feigin, A.P. Veselov, Quasiinvariants of Coxeter groups and m-harmonic polynomials, Int. Math. Res. Not. 10 (2002) 521–545], bases for m-quasiinvariants were computed for dihedral groups, including S3, and Felder and Veselov [G. Felder, A.P. Veselov, Action of Coxeter groups on m-harmonic polynomials and Knizhnik–Zamolodchikov equations, Mosc. Math. J. 4 (2003) 1269–1291] also computed the non-symmetric m-quasiinvariants of lowest degree for general Sn. In this paper, we provide a new characterization of the m-quasiinvariants of Sn, and use this to provide a basis for the isotypic component indexed by the partition [n−1,1]. This builds on a previous paper, [J. Bandlow, G. Musiker, Quasiinvariants of S3, J. Combin. Theory Ser. A 109 (2005) 281–298], in which we computed a basis for S3 via combinatorial methods
- …
