The involution principle and h-positive symmetric functions
Name
50147615-MIT.pdf
Description
Full printable version
Size
3.67 MB
Format
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Checksum (MD5)
f4e001ce52b7b4e69312d1a8c51d6527
Author(s)
Joseph, Benjamin S., 1976-
Advisor(s)
Richard P. Stanley.
Date Issued
2001
Publisher
Massachusetts Institute of Technology
Abstract
The criterion of h-positivity corresponds to the criterion that a polynomial representation of the general linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function as a power series yields coefficients whose positivity implies the h-positivity of the characteristic of the symmetric group character whose value on the permutation w is the number of labeled forests with c(w) vertices, where c(w) is the number of cycles of w. Another example of an h-positive symmetric function is the characteristic of the top homology of the even-ranked subposet of the partition lattice. In this case, the positive coefficients of the characteristic refine the tangent number E₂nâ‚‹₁ into sums of powers of two.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 65).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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