The involution principle and h-positive symmetric functions

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 E₂n₋₁ into sums of powers of two.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2001

Author dc:creator

• Joseph, Benjamin S., 1976-

Advisor dc:contributor.advisor

• Richard P. Stanley.

• Mathematics.

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• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

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• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

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http://hdl.handle.net/1721.1/8225

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/8225