Geodesic
Long Sets of Lengths With Maximal Elasticity
Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1284-1318

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DOI

We introduce a newinvariant describing the structure of sets of lengths in atomicmonoids and domains. For an atomic monoid $H$ , let ${{\Delta }_{\rho }}\left( H \right)$ be the set of all positive integers d that occur as differences of arbitrarily long arithmetical progressions contained in sets of lengths havingmaximal elasticity $\rho \left( H \right)$ . We study ${{\Delta }_{\rho }}\left( H \right)$ 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.
DOI : 10.4153/CJM-2017-043-4
Mots-clés : 13A05, 13F05, 16H10, 16U30, 20M13, transfer Krull monoid, weakly Krull monoid, set of length, elasticity 
Geroldinger, Alfred; Zhong, Qinghai. Long Sets of Lengths With Maximal Elasticity. Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1284-1318. doi: 10.4153/CJM-2017-043-4
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     author = {Geroldinger, Alfred and Zhong, Qinghai},
     title = {Long {Sets} of {Lengths} {With} {Maximal} {Elasticity}},
     journal = {Canadian journal of mathematics},
     pages = {1284--1318},
     year = {2018},
     volume = {70},
     number = {6},
     doi = {10.4153/CJM-2017-043-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-043-4/}
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