The number of symmetric chain decompositions

2024/05/15 by István Tomon, Tomon, István
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2405.09322

openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the number of symmetric chain decompositions of the Boolean lattice 2^[n] is ((n)/(2e)+o(n))²ⁿ. Furthermore, the number of symmetric chain decompositions of the hypergrid [t]ⁿ is n^{(1-o_n(1))⋅ tn}.

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