On conjectures of Foulkes, Siemons and Wagner and Stanley
Let A = (AI, ... ,Ar ) be a partition of n. An unordered A-tabloid is a partition of the set {I, 2, ... , n} into r pairwise disjoint sets of sizes AI, ,Ar . Let F denote the field of complex numbers and C the symmetric group of {I, 2, , n}. Define HA to be the permutation module of FC whose basis i...
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University of East Anglia
2008
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ndltd-bl.uk-oai-ethos.bl.uk-4906722015-03-20T03:15:54ZOn conjectures of Foulkes, Siemons and Wagner and StanleyMcKay, Thomas J.2008Let A = (AI, ... ,Ar ) be a partition of n. An unordered A-tabloid is a partition of the set {I, 2, ... , n} into r pairwise disjoint sets of sizes AI, ,Ar . Let F denote the field of complex numbers and C the symmetric group of {I, 2, , n}. Define HA to be the permutation module of FC whose basis is the set of unordered A-tabloids. Foulkes conjectured in [13] that there exists an injective FC-homomorphism H(b a ) -t H(a b ) when a ::; b. Independently Siemons and Wagner [27] and Stanley [29] generalized this conjecture to ask if there exists an injective map HA -t HA'. In this thesis we investigate these conjectures.510University of East Angliahttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490672https://ueaeprints.uea.ac.uk/38272/Electronic Thesis or Dissertation |
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510 |
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510 McKay, Thomas J. On conjectures of Foulkes, Siemons and Wagner and Stanley |
| description |
Let A = (AI, ... ,Ar ) be a partition of n. An unordered A-tabloid is a partition of the set {I, 2, ... , n} into r pairwise disjoint sets of sizes AI, ,Ar . Let F denote the field of complex numbers and C the symmetric group of {I, 2, , n}. Define HA to be the permutation module of FC whose basis is the set of unordered A-tabloids. Foulkes conjectured in [13] that there exists an injective FC-homomorphism H(b a ) -t H(a b ) when a ::; b. Independently Siemons and Wagner [27] and Stanley [29] generalized this conjecture to ask if there exists an injective map HA -t HA'. In this thesis we investigate these conjectures. |
| author |
McKay, Thomas J. |
| author_facet |
McKay, Thomas J. |
| author_sort |
McKay, Thomas J. |
| title |
On conjectures of Foulkes, Siemons and Wagner and Stanley |
| title_short |
On conjectures of Foulkes, Siemons and Wagner and Stanley |
| title_full |
On conjectures of Foulkes, Siemons and Wagner and Stanley |
| title_fullStr |
On conjectures of Foulkes, Siemons and Wagner and Stanley |
| title_full_unstemmed |
On conjectures of Foulkes, Siemons and Wagner and Stanley |
| title_sort |
on conjectures of foulkes, siemons and wagner and stanley |
| publisher |
University of East Anglia |
| publishDate |
2008 |
| url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490672 |
| work_keys_str_mv |
AT mckaythomasj onconjecturesoffoulkessiemonsandwagnerandstanley |
| _version_ |
1716779568104210432 |