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- W3136292371 abstract "Let D = {i₁, i₂,..., in} be a set of n positive integers. A Skolem-type sequenceof order n is a sequence of i such that every i ∈ D appears exactly twice in thesequence at position aᵢ and bᵢ, and |bᵢ - aᵢ| = i. These sequences might containempty positions, which are filled with 0 elements and called hooks. For example,(2; 4; 2; 0; 3; 4; 0; 3) is a Skolem-type sequence of order n = 3, D = f2; 3; 4g and twohooks. If D = f1; 2; 3; 4g we have (1; 1; 4; 2; 3; 2; 4; 3), which is a Skolem-type sequenceof order 4 and zero hooks, or a Skolem sequence.In this thesis we introduce additional disjoint Skolem-type sequences of order nsuch as disjoint (hooked) near-Skolem sequences and (hooked) Langford sequences.We present several tables of constructions that are disjoint with known constructionsand prove that our constructions yield Skolem-type sequences. We also discuss thenecessity and sufficiency for the existence of Skolem-type sequences of order n wheren is positive integers." @default.
- W3136292371 created "2021-03-29" @default.
- W3136292371 creator A5085491274 @default.
- W3136292371 date "2018-01-01" @default.
- W3136292371 modified "2023-09-29" @default.
- W3136292371 title "Disjoint skolem-type sequences and applications" @default.
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- W3136292371 hasPublicationYear "2018" @default.
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