The $h$-vectors of 1-dimensional Matroid Complexes and a Conjecture of Stanley

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dc.creatorStokes, Erik
dc.date2009-03-20
dc.date.accessioned2026-07-07T12:54:51Z
dc.date.available2026-07-07T12:54:51Z
dc.descriptionA matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible $h$-vectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question. We also prove the 1-dimensional case of a conjecture of Stanley that all matroid $h$-vectors are pure ${O}$-sequences. Finally, we completely characterize the Stanley-Reisner ideals of 1-dimensional matroid complexes.
dc.description24 pages with 2 figures. submitted to J. Algebraic Comb
dc.identifierhttps://arxiv.org/abs/0903.3569
dc.identifierhttp://arxiv.org/abs/0903.3569
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224078
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13F55 (Primary) 05B35 (Secondary)
dc.titleThe $h$-vectors of 1-dimensional Matroid Complexes and a Conjecture of Stanley
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