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Peer-reviewedCC BY 4.0Forum of Mathematics, Sigma

Complementary vectors of simplicial complexes

  • Matt Larson1
  • Alan Stapledon2
  1. 1Princeton University
  2. 2Sydney Mathematics Research Institute
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Abstract

We classify the complementary vectors of doubly Cohen–Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives new bounds on the number of independent sets in a matroid. Our technique works more generally for certain level quotients of Stanley–Reisner rings, giving new bounds on the face numbers of Buchsbaum* complexes.

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Cite

BibTeXRIS
BibTeX
@article{larson2026complementary,
  title = {{Complementary vectors of simplicial complexes}},
  author = {Matt Larson and Alan Stapledon},
  journal = {Forum of Mathematics, Sigma},
  year = {2026},
  month = oct,
  doi = {10.1017/fms.2026.10288},
  url = {https://www.cambridge.org/core/product/identifier/S2050509426102886/type/journal_article},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Complementary vectors of simplicial complexes
AU  - Matt Larson
AU  - Alan Stapledon
PY  - 2026
DA  - 2026/10/02
JO  - Forum of Mathematics, Sigma
DO  - 10.1017/fms.2026.10288
UR  - https://www.cambridge.org/core/product/identifier/S2050509426102886/type/journal_article
AB  - We classify the complementary vectors of doubly Cohen–Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives new bounds on the number of independent sets in a matroid. Our technique works more generally for certain level quotients of Stanley–Reisner rings, giving new bounds on the face numbers of Buchsbaum* complexes.
SN  - 2050-5094
ER  -