1,720,961 research outputs found
Counting subrings of Zn of index k
No full textAbstractWe consider the problem of determining the number of subrings of the ring Zn of a fixed index k, denoted fn(k). We present a decomposition theorem for these subrings and calculate explicit expressions for the Dirichlet series generating function Fn(s)=∑k=1∞fn(k)k−s for n⩽4 and for the generating function Φp(x,y)=∑e=0∞∑n=0∞fn(pe)xeyn/n! modulo p. We also calculate fn(k) when k is not divisible by the sixth power of any prime
Specht modules and Schubert varieties for general diagrams
Get PDFThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 87-88).The algebra of symmetric functions, the representation theory of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these objects to allow for not just Young diagrams but arbitrary collections of boxes or, equally well, bipartite graphs. We will then provide evidence for a conjecture that the relation between the areas described above can be extended to these general diagrams. In particular, we will prove the conjecture for forests. Along the way, we will use a novel geometric approach to show that the dimension of the Specht module of a forest is the same as the normalized volume of its matching polytope. We will also demonstrate a new Littlewood-Richardson rule and provide combinatorial, algebraic, and geometric interpretations of it.by Ricky Ini Liu.Ph.D
Plane partitions and rowmotion on rectangular and trapezoidal posets
No full textWe define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a result by Proctor. We also show that this map is equivariant with respect to birational rowmotion, resolving a conjecture of Williams and implying that birational rowmotion on trapezoidal posets has finite order.</p
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Piecewise-linear promotion and RSK in rectangles and moon polyominoes
Get PDFWe study piecewise-linear and birational lifts of Schützenberger promotion, evacuation, and the RSK correspondence defined in terms of toggles. Using this perspective, we prove that certain chain statistics in rectangles shift predictably under the action of these maps. We then use this to construct piecewise-linear and birational versions of Rubey's bijections between fillings of equivalent moon polyominoes that preserve these chain statistics, and we show that these maps form a commuting diagram. We also discuss how these results imply Ehrhart equivalence and Ehrhart quasi-polynomial period collapse of certain analogues of chain polytopes for moon polyominoes.Mathematics Subject Classifications: 05E18, 05A05, 05A19, 52B05Keywords: Birational rowmotion, Robinson-Schensted-Knuth correspondence, moon polyominoes, period collaps
Piecewise-linear promotion and RSK in rectangles and moon polyominoes
Get PDFWe study piecewise-linear and birational lifts of Sch\"utzenberger promotion,
evacuation, and the RSK correspondence defined in terms of toggles. Using this
perspective, we prove that certain chain statistics in rectangles shift
predictably under the action of these maps. We then use this to construct
piecewise-linear and birational versions of Rubey's bijections between fillings
of equivalent moon polyominoes that preserve these chain statistics, and we
show that these maps form a commuting diagram. We also discuss how these
results imply Ehrhart equivalence and Ehrhart quasi-polynomial period collapse
of certain analogues of chain polytopes for moon polyominoes
Plane partitions and rowmotion on rectangular and trapezoidal posets
No full textWe define a birational map between labelings of a rectangular poset and its
associated trapezoidal poset. This map tropicalizes to a bijection between the
plane partitions of these posets of fixed height, giving a new bijective proof
of a result by Proctor. We also show that this map is equivariant with respect
to birational rowmotion, resolving a conjecture of Williams and implying that
birational rowmotion on trapezoidal posets has finite order.Comment: 40 pages, 17 figure
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
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