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math.CT2024★ 1 cited
Convex decomposition spaces and Crapo complementation formula
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We establish a Crapo complementation formula for the Möbius function in a general decomposition space in terms of a convex subspace and its complement: $μ^X \simeq μ^…
math.CO2024
Noncrossing arithmetic
Kurusch Ebrahimi-Fard, Loïc Foissy, Joachim Kock +1
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory…