Enumerating numerical sets associated to a numerical semigroup Article Swipe
April Chen
,
Nathan O. Kaplan
,
Liam Lawson
,
Christopher O’Neill
,
Deepesh Singhal
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1016/j.dam.2023.08.010
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1016/j.dam.2023.08.010
A numerical set T is a subset of N0 that contains 0 and has finite complement. The atom monoid of T is the set of x∈N0 such that x+T⊆T. Marzuola and Miller introduced the anti-atom problem: how many numerical sets have a given atom monoid? This is equivalent to asking for the number of integer partitions with a given set of hook lengths. We introduce the void poset of a numerical semigroup S and show that numerical sets with atom monoid S are in bijection with certain order ideals of this poset. We use this characterization to answer the anti-atom problem when S has small type.
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- article
- Language
- en
- Landing Page
- https://doi.org/10.1016/j.dam.2023.08.010
- OA Status
- hybrid
- References
- 15
- Related Works
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- OpenAlex ID
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https://doi.org/10.1016/j.dam.2023.08.010Digital Object Identifier
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Enumerating numerical sets associated to a numerical semigroupWork title
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articleOpenAlex work type
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enPrimary language
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2023Year of publication
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2023-09-03Full publication date if available
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April Chen, Nathan O. Kaplan, Liam Lawson, Christopher O’Neill, Deepesh SinghalList of authors in order
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https://doi.org/10.1016/j.dam.2023.08.010Publisher landing page
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YesWhether a free full text is available
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hybridOpen access status per OpenAlex
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https://doi.org/10.1016/j.dam.2023.08.010Direct OA link when available
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Mathematics, Monoid, Bijection, Partially ordered set, Combinatorics, Numerical semigroup, Free monoid, Semigroup, Discrete mathematics, Atom (system on chip), Set (abstract data type), Computer science, Programming language, Embedded systemTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.We | 63, 92 |
| abstract_inverted_index.in | 83 |
| abstract_inverted_index.is | 4, 21, 46 |
| abstract_inverted_index.of | 7, 19, 24, 53, 60, 68, 89 |
| abstract_inverted_index.to | 48, 96 |
| abstract_inverted_index.The | 16 |
| abstract_inverted_index.and | 12, 30, 73 |
| abstract_inverted_index.are | 82 |
| abstract_inverted_index.for | 50 |
| abstract_inverted_index.has | 13, 103 |
| abstract_inverted_index.how | 36 |
| abstract_inverted_index.set | 2, 23, 59 |
| abstract_inverted_index.the | 22, 33, 51, 65, 98 |
| abstract_inverted_index.use | 93 |
| abstract_inverted_index.This | 45 |
| abstract_inverted_index.atom | 17, 43, 79 |
| abstract_inverted_index.have | 40 |
| abstract_inverted_index.hook | 61 |
| abstract_inverted_index.many | 37 |
| abstract_inverted_index.sets | 39, 77 |
| abstract_inverted_index.show | 74 |
| abstract_inverted_index.such | 26 |
| abstract_inverted_index.that | 9, 27, 75 |
| abstract_inverted_index.this | 90, 94 |
| abstract_inverted_index.void | 66 |
| abstract_inverted_index.when | 101 |
| abstract_inverted_index.with | 56, 78, 85 |
| abstract_inverted_index.given | 42, 58 |
| abstract_inverted_index.order | 87 |
| abstract_inverted_index.poset | 67 |
| abstract_inverted_index.small | 104 |
| abstract_inverted_index.type. | 105 |
| abstract_inverted_index.Miller | 31 |
| abstract_inverted_index.answer | 97 |
| abstract_inverted_index.asking | 49 |
| abstract_inverted_index.finite | 14 |
| abstract_inverted_index.ideals | 88 |
| abstract_inverted_index.monoid | 18, 80 |
| abstract_inverted_index.number | 52 |
| abstract_inverted_index.poset. | 91 |
| abstract_inverted_index.subset | 6 |
| abstract_inverted_index.x∈N0 | 25 |
| abstract_inverted_index.certain | 86 |
| abstract_inverted_index.integer | 54 |
| abstract_inverted_index.monoid? | 44 |
| abstract_inverted_index.problem | 100 |
| abstract_inverted_index.Marzuola | 29 |
| abstract_inverted_index.contains | 10 |
| abstract_inverted_index.lengths. | 62 |
| abstract_inverted_index.problem: | 35 |
| abstract_inverted_index.x+T⊆T. | 28 |
| abstract_inverted_index.anti-atom | 34, 99 |
| abstract_inverted_index.bijection | 84 |
| abstract_inverted_index.introduce | 64 |
| abstract_inverted_index.numerical | 1, 38, 70, 76 |
| abstract_inverted_index.semigroup | 71 |
| abstract_inverted_index.equivalent | 47 |
| abstract_inverted_index.introduced | 32 |
| abstract_inverted_index.partitions | 55 |
| abstract_inverted_index.complement. | 15 |
| abstract_inverted_index.characterization | 95 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5003995796 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 5 |
| corresponding_institution_ids | https://openalex.org/I26538001 |
| citation_normalized_percentile.value | 0.26828815 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |