{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/8225"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/8225","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The involution principle and h-positive symmetric functions","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 E₂n₋₁ into sums of powers of two.","abstract_html":"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.","abstract_has_math":false,"creators":["Joseph, Benjamin S., 1976-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Richard P. Stanley."],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001","date_published":"2001","updated_at":"2026-07-22T22:21:36Z","subjects":["Mathematics."],"languages":["eng"],"rights":["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. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The involution principle and h-positive symmetric functions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Richard P. Stanley."],"dc:contributor.department":["Massachusetts Institute of Technology. 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