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arXiv · 1706.06907

Long sets of lengths with maximal elasticity

Alfred Geroldinger·Qinghai Zhong
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Abstract

We introduce a new invariant describing the structure of sets of lengths in atomic monoids and domains. For an atomic monoid $H$, let $Δ_ρ (H)$ be the set of all positive integers $d$ which occur as differences of arbitrarily long arithmetical progressions contained in sets of lengths having maximal elasticity $ρ(H)$. We study $Δ_ρ (H)$ for transfer Krull monoids of finite type (including commutative Krull domains with finite class group) with methods from additive combinatorics, and also for a class of weakly Krull domains (including orders in algebraic number fields) for which we use ideal theoretic methods.

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Alfred Geroldinger, Qinghai Zhong. 2017-09-28. Long sets of lengths with maximal elasticity. https://doi.org/10.4153/cjm-2017-043-4

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