On the number of [formula omitted]-arithmetic expressions in [formula omitted] distinct variables.
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| Title: | On the number of [formula omitted]-arithmetic expressions in [formula omitted] distinct variables. |
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| Authors: | Stošić, Ivan1 (AUTHOR), Ranđelović, Žarko2,3 (AUTHOR), Damnjanović, Ivan1,4,5,6 (AUTHOR) ivan.damnjanovic@famnit.upr.si |
| Source: | Discrete Applied Mathematics. Jun2026, Vol. 386, p279-292. 14p. |
| Subjects: | Arithmetic, Independent variables, Parameterization, Algebraic field theory, Computational complexity, Applied mathematics |
| Abstract: | How many arithmetic expressions are there in n distinct variables? In this paper, we provide a Θ (n 2) algorithm for computing this number for arithmetic expressions over an arbitrary field F. We consider several cases of this problem with various restrictions on the allowed operations. An expression tree is an ordered rooted tree whose internal nodes represent operations to be performed, while its leaves correspond to formal variables from a set X. We view any arithmetic expression as an element of F (X) that is obtained by evaluating an expression tree. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192967414 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the number of [formula omitted]-arithmetic expressions in [formula omitted] distinct variables. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Stošić%2C+Ivan%22">Stošić, Ivan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ranđelović%2C+Žarko%22">Ranđelović, Žarko</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Damnjanović%2C+Ivan%22">Damnjanović, Ivan</searchLink><relatesTo>1,4,5,6</relatesTo> (AUTHOR)<i> ivan.damnjanovic@famnit.upr.si</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jun2026, Vol. 386, p279-292. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Arithmetic%22">Arithmetic</searchLink><br /><searchLink fieldCode="DE" term="%22Independent+variables%22">Independent variables</searchLink><br /><searchLink fieldCode="DE" term="%22Parameterization%22">Parameterization</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+field+theory%22">Algebraic field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Applied+mathematics%22">Applied mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: How many arithmetic expressions are there in n distinct variables? In this paper, we provide a Θ (n 2) algorithm for computing this number for arithmetic expressions over an arbitrary field F. We consider several cases of this problem with various restrictions on the allowed operations. An expression tree is an ordered rooted tree whose internal nodes represent operations to be performed, while its leaves correspond to formal variables from a set X. We view any arithmetic expression as an element of F (X) that is obtained by evaluating an expression tree. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.02.011 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 279 Subjects: – SubjectFull: Arithmetic Type: general – SubjectFull: Independent variables Type: general – SubjectFull: Parameterization Type: general – SubjectFull: Algebraic field theory Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Applied mathematics Type: general Titles: – TitleFull: On the number of [formula omitted]-arithmetic expressions in [formula omitted] distinct variables. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Stošić, Ivan – PersonEntity: Name: NameFull: Ranđelović, Žarko – PersonEntity: Name: NameFull: Damnjanović, Ivan IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 386 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
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