REALISABLE SETS OF CATENARY DEGREES OF NUMERICAL MONOIDS
2017 ◽
Vol 97
(2)
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pp. 240-245
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The catenary degree is an invariant that measures the distance between factorisations of elements within an atomic monoid. In this paper, we classify which finite subsets of$\mathbb{Z}_{\geq 0}$occur as the set of catenary degrees of a numerical monoid (that is, a co-finite, additive submonoid of$\mathbb{Z}_{\geq 0}$). In particular, we show that, with one exception, every finite subset of$\mathbb{Z}_{\geq 0}$that can possibly occur as the set of catenary degrees of some atomic monoid is actually achieved by a numerical monoid.
2014 ◽
Vol 97
(3)
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pp. 289-300
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Keyword(s):
ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE
2004 ◽
Vol 04
(01)
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pp. 63-76
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Keyword(s):
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1968 ◽
Vol 64
(1)
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pp. 3-4
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Keyword(s):
2007 ◽
Vol 143
(6)
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pp. 1493-1510
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Keyword(s):
2007 ◽
Vol 59
(2)
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pp. 343-371
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2019 ◽
Vol 29
(03)
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pp. 419-457
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Keyword(s):
1984 ◽
Vol 95
(1)
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pp. 21-23