More refined enumerations of alternating sign matrices

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dc.creatorFischer, Ilse
dc.creatorRomik, Dan
dc.date2009-03-29
dc.date2009-04-15
dc.date.accessioned2026-07-07T13:03:37Z
dc.date.available2026-07-07T13:03:37Z
dc.descriptionWe study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the first row, and more general "d-refined" enumerations of ASMs according to the first d rows. For the doubly-refined case of d=2, we derive a system of linear equations satisfied by the doubly-refined enumeration numbers A_{n,i,j} that enumerate such matrices. We give a conjectural explicit formula for A_{n,i,j} and formulate several other conjectures about the sufficiency of the linear equations to determine the A_{n,i,j}'s and about an extension of the linear equations to the general d-refined enumerations.
dc.description38 pages; added references and made minor changes to the introduction; source files now inlcude the Mathematica package RefinedASM
dc.identifierhttps://arxiv.org/abs/0903.5073
dc.identifierhttp://arxiv.org/abs/0903.5073
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226869
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subject05A15
dc.titleMore refined enumerations of alternating sign matrices
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