1,721,113 research outputs found
Proof of Two Conjectures of Brenti and Simion on Kazhdan-Lusztig Polynomials
No full textWe find an explicit formula for the Kazhdan-Lusztig polynomials Pui a, vi of the symmetric group fraktur G sign(n) where, for a, i, n ∈ N such that 1 ≤ a ≤ i ≤ n, we denote by ui,a = s asa+1 script G sign si-1 and by vi the element of fraktur G sign(n) obtained by inserting n in position i in any permutation of fraktur G sign(n - 1) allowed to lise only in the first and in the last place Our result implies, in particular, the validity of two conjectures of Brenti and Simion [4, Conjectures 4.2 and 4.3], and includes as a special case a result of Shapiro, Shapiro and Vainshtein [13, Theorem 1] All the proofs are purely combinatorial and make no use of the geometry of the corresponding Schubert varieties
Special matchings in Coxeter groups
No full textSpecial matchings are purely combinatorial objects associated with a partially ordered set, which have applications in Coxeter group theory. We provide an explicit characterization and a complete classification of all special matchings of any lower Bruhat interval. The results hold in any arbitrary Coxeter group and have also applications in the study of the corresponding parabolic Kazhdan–Lusztig polynomials
Classification of finite irreducible conformal modules for K'_4
Full text linkWe classify finite irreducible modules over the conformal superalgebra K′_4 by their correspondence with finite conformal modules over the
associated annihilation superalgebra A(K′_4). This is achieved by a complete classification of singular vectors in generalized Verma modules
for A(K′_4). We also show that morphisms between generalized Verma modules can be arranged in infinitely many bilateral complexe
Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials
Full text linkWe give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the Kazhdan–Lusztig polynomials which holds in complete generality and is simpler and more explicit than any existing one. We point out that, in a certain sense, this formula cannot be simplified
A simple characterization of special matchings in lower Bruhat intervals
Full text linkWe give a simple characterization of special matchings in lower Bruhat intervals (that is, intervals starting from the identity element) of a Coxeter group. As a byproduct, we obtain some results on the action of special matchings.
The generalized lifting property of Bruhat intervals
Full text linkIn Tsukerman and Williams (Adv Math 285: 766–810, 2015), it is shown that every Bruhat interval of the symmetric group satisfies the so-called generalized lifting property. In this paper, we show that a Coxeter group satisfies this property if and only if it is finite and simply-laced
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
Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids
Full text linkWe provide a weaker version of the generalized lifting property that holds in complete
generality for all Coxeter groups, and we use it to show that every parabolic Bruhat
interval of a finite Coxeter group is a Coxeter matroid. We also describe some
combinatorial properties of the associated polytope
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