{"data":{"id":"10.6084/m9.figshare.156290.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.156290.v1","prefix":"10.6084","suffix":"m9.figshare.156290.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Locey, Kenneth","nameType":"Personal","givenName":"Kenneth","familyName":"Locey","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Random integer partitions with restricted numbers of parts"}],"publisher":"figshare","container":{},"publicationYear":2013,"subjects":[{"subject":"Statistics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Computational Biology"},{"subject":"Probability"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Algebra"},{"subject":"Theoretical Computer Science"},{"subject":"Applied Computer Science"}],"contributors":[],"dates":[{"date":"2013-02-09","dateType":"Created"},{"date":"2016-01-11","dateType":"Updated"},{"date":"2013","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsPreviousVersionOf","relatedIdentifier":"10.6084/m9.figshare.156290","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["0 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"A preprint of a manuscript revealing a conceptually simple and comparatively fast algorithm for generating uniform random integer partitions. Currently, no mathematical software includes a function to do this and from combing the literature and peer help cites (stackexchange), it doesn't appear that this problem has ever been solved. It, at least, has not been implemented into a straightforward computing algorithm. I derive the algorithm, provide a generic code representation for it, provide a specific Python based implementation, and compare the performance to the random partitioning function of Sage (a powerful and generally very fast computer algebra environment). Finally, and the reason I tagged macroecology, maxent, and economics, I reveal how random integer partitioning algorithms can be used to address current and meaningful problems in the natural and social sciences. \u003cstrong\u003e I would greatly appreciate your constructive and insightful comments.\u003c/strong\u003e Additionally, the following provided some of the reason for posting this on figshare: \u003cstrong\u003ehttp://emckiernan.wordpress.com/2012/09/21/why-i-chose-figshare-for-my-homeless-manuscript/\u003c/strong\u003e","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/articles/dataset/Random_integer_partitions_with_restricted_numbers_of_parts/156290/1","contentUrl":null,"metadataVersion":4,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2016-01-11T15:58:34.000Z","registered":"2016-01-11T15:58:35.000Z","published":"2013","updated":"2020-09-05T02:50:10.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.156290.v1","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versi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