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.
From: Matt Larson [view email]
[v1]
Mon, 28 Apr 2025 21:09:48 UTC (22 KB)
[v2]
Sun, 13 Sep 2026 19:53:22 UTC (23 KB)
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