{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-2121"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-2121","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"The head and tail conjecture for alternating knots","abstract":"The colored Jones polynomial is an invariant of knots and links, which produces a sequence of Laurent polynomials. In this work, we study new power series link invariants, derived from the colored Jones polynomial, called its head and tail. We begin with a brief survey of knot theory and the colored Jones polynomial in particular. In Chapter 3, we use skein theory to prove that for adequate links, the n-th leading coefficient of the N-th colored Jones polynomial stabilizes when viewed as a sequence in N. This property allows us to define the head and tail for adequate links. In Chapter 4 we show a class of knots with trivial tail, and in Chapter 5 we develop techniques to calculate the head and tail for various knots and links using a graph derived from the link diagram.","abstract_html":"The colored Jones polynomial is an invariant of knots and links, which produces a sequence of Laurent polynomials. In this work, we study new power series link invariants, derived from the colored Jones polynomial, called its head and tail. We begin with a brief survey of knot theory and the colored Jones polynomial in particular. In Chapter 3, we use skein theory to prove that for adequate links, the n-th leading coefficient of the N-th colored Jones polynomial stabilizes when viewed as a sequence in N. This property allows us to define the head and tail for adequate links. In Chapter 4 we show a class of knots with trivial tail, and in Chapter 5 we develop techniques to calculate the head and tail for various knots and links using a graph derived from the link diagram.","abstract_has_math":false,"creators":["Armond, Cody"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:58:50Z","subjects":["knot theory","colored Jones polynomial","skein theory","head and tail","adequate links"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-07032012-165733","https://repository.lsu.edu/gradschool_dissertations/1122"],"render_values":[{"text":"etd-07032012-165733","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/1122","href":"https://repository.lsu.edu/gradschool_dissertations/1122","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.1122","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Armond, Cody"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-03-27"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:11:05Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["knot theory","colored Jones polynomial","skein theory","head and tail","adequate links"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-07032012-165733","10.31390/gradschool_dissertations.1122","https://repository.lsu.edu/gradschool_dissertations/1122"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The colored Jones polynomial is an invariant of knots and links, which produces a sequence of Laurent polynomials. In this work, we study new power series link invariants, derived from the colored Jones polynomial, called its head and tail. We begin with a brief survey of knot theory and the colored Jones polynomial in particular. In Chapter 3, we use skein theory to prove that for adequate links, the n-th leading coefficient of the N-th colored Jones polynomial stabilizes when viewed as a sequence in N. This property allows us to define the head and tail for adequate links. In Chapter 4 we show a class of knots with trivial tail, and in Chapter 5 we develop techniques to calculate the head and tail for various knots and links using a graph derived from the link diagram."]},{"key":"dc:title","label":"Title","values":["The head and tail conjecture for alternating knots"]}]}],"canonical_facts":{"dc:creator":["Armond, Cody"],"dc:date":["2012-03-27"],"dc:date.available":["2022-05-12T23:11:05Z"],"dc:description.abstract":["The colored Jones polynomial is an invariant of knots and links, which produces a sequence of Laurent polynomials. In this work, we study new power series link invariants, derived from the colored Jones polynomial, called its head and tail. We begin with a brief survey of knot theory and the colored Jones polynomial in particular. In Chapter 3, we use skein theory to prove that for adequate links, the n-th leading coefficient of the N-th colored Jones polynomial stabilizes when viewed as a sequence in N. This property allows us to define the head and tail for adequate links. In Chapter 4 we show a class of knots with trivial tail, and in Chapter 5 we develop techniques to calculate the head and tail for various knots and links using a graph derived from the link diagram."],"dc:identifier":["etd-07032012-165733","10.31390/gradschool_dissertations.1122","https://repository.lsu.edu/gradschool_dissertations/1122"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["knot theory","colored Jones polynomial","skein theory","head and tail","adequate links"],"dc:title":["The head and tail conjecture for alternating knots"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:58:50Z"}