Séminaire Lotharingien de Combinatoire, 95B.6 (2026), 11 pp.
Matt Larson and Alan Stapledon
Complementary Vectors of Doubly Cohen-Macaulay Complexes
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.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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