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• W2163164390 abstract "Given a sequence of integers aj, j ⩾ 1, a multiset is a combinatorial object composed of unordered components, such that there are exactly aj one-component multisets of size j. When aj ≍ jr−1 yj for some r > 0, y ⩾ 1, then the multiset is called expansive. Let cn be the number of multisets of total size n. Using a probabilistic approach, we prove for expansive multisets that cn/cn+1 → 1 and that cn/cn+1 < 1 for large enough n. This allows us to prove monadic second-order limit laws for expansive multisets. The above results are extended to a class of expansive multisets with oscillation. Moreover, under the condition aj = Kjr−1 yj + O(yν j), where K > 0, r > 0, y > 1, ν ∈ (0, 1), we find an explicit asymptotic formula for cn. In a similar way we study the asymptotic behavior of selections, which are defined as combinatorial objects composed of unordered components of distinct sizes." @default.
• W2163164390 created "2016-06-24" @default.
• W2163164390 creator A5052564891 @default.
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• W2163164390 date "2006-02-01" @default.
• W2163164390 modified "2023-10-14" @default.
• W2163164390 title "ASYMPTOTIC ENUMERATION AND LOGICAL LIMIT LAWS FOR EXPANSIVE MULTISETS AND SELECTIONS" @default.
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• W2163164390 doi "https://doi.org/10.1112/s0024610705022477" @default.
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