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Pieri's formula for generalized Schur polynomials(The world of Combinatorial Representation Theory)
Get PDFOn an edge-signed generalization of chordal graphs and free multiplicities on braid arrangements (Representation Theory and Combinatorics)
Get PDFOn a bijective proof of a factorization formula for Macdonald polynomials at roots of unity (Expansion of Combinatorial Representation Theory)
Get PDFTabloids and weighted sums of characters of certain modules of the symmetric groups
Get PDFWe consider certain modules of the symmetric groups whose basis elements are called tabloids. Some of these modules are isomorphic to subspaces of the cohomology rings of subvarieties of flag varieties as modules of the symmetric groups. We give a combinatorial description for some weighted sums of their characters, i.e., we introduce combinatorial objects called (½; l)-tableaux and rewrite weighted sums of characters as the numbers of these combinatorial objects. We also consider the meaning of these combinatorial objects, i.e., we construct a correspondence between (½; l)-tableaux and tabloids whose images are eigenvectors of the action of an element of cycle type ½ in quotient modules
Pieri's formula for generalized Schur polynomials
Get PDFYoung's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutating relation of generalized Schur operators implies Pieri's formula to generalized Schur polynomials
On moments of the noncentral Wishart distributions and weighted generating functions of matchings (Combinatorial Representation Theory and its Applications)
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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
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