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Replacement Young combination of tables Properties and Applications

Author: SunYi
Tutor: MengJiXiang；ChenYongChuan
School: Xinjiang University
Course: Applied Mathematics
Keywords: Replacement Yang Table Arrangement Staggered Bijection
CLC: O157
Type: Master's thesis
Year: 2011
Downloads: 39
Quote: 0
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Abstract


In the field of combinatorial mathematics , Young diagram (Young diagram) is very important and wide-reaching combination of one of the objects . Based on the Young diagram (Young diagram) , based on the introduction and study of a new combination of objects - tables replacing Yang (permutation tableau). replacement Yang A. Postnikov table is essentially a completely non-negative Grassnann in the study of cellular and cellular decomposition defined ] - chart (]-diagram) is a subset . LK Williams and E.Steingr '(?) msson find it and ordered one relationship exists naturally , they put their depth from which the independent study , because replacement Yang table has a visual image of the structural features , we first examine its basic structure, and then through the establishment of replacement Yang from tables to -one mapping between the arrangement to study the nature of its composition and its field of application of the combined counts . article first studied the permutation Young and number of the basic structure of the table , followed by simplifying LKWilliams and E. Steingr '(?) msson created from tables to arrange replacement Yang -one mapping between Ψ, and gives a proof Ψ is bijective new method that we found this new approach : for any one permutation π ∈ S_n, can be written as the product of some form of circle , and each circle elements are arranged in descending order . Finally, in the application of replacement Yang table , we studied a collection of [2n] with n on staggered fixed point corresponding permutation Young sheets set [n] on the wrong row corresponding permutation Young relationships between tables , and found that there is a correspondence between them . Using this correspondence, we gives the following conjecture proved R.Stanley a new approach : A_ \n 1) / 2 , \has k fixed points of the anti- staggered number.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics )
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