Integer compositions with part sizes not exceeding k
We study the compositions of an integer n whose part sizes do not exceed a fixed integer k. We use the methods of analytic combinatorics to obtain precise asymptotic formulas for the number of such compositions, the total number of parts among all such compositions, the expected number of parts in s...
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| creator | Malandro, Martin E |
| description | We study the compositions of an integer n whose part sizes do not exceed a
fixed integer k. We use the methods of analytic combinatorics to obtain precise
asymptotic formulas for the number of such compositions, the total number of
parts among all such compositions, the expected number of parts in such a
composition, the total number of times a particular part size appears among all
such compositions, and the expected multiplicity of a given part size in such a
composition. Along the way we also obtain recurrences and generating functions
for calculating several of these quantities. Our results also apply to
questions about certain kinds of tilings and rhythm patterns. |
| doi_str_mv | 10.48550/arxiv.1108.0337 |
| format | Article |
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fixed integer k. We use the methods of analytic combinatorics to obtain precise
asymptotic formulas for the number of such compositions, the total number of
parts among all such compositions, the expected number of parts in such a
composition, the total number of times a particular part size appears among all
such compositions, and the expected multiplicity of a given part size in such a
composition. Along the way we also obtain recurrences and generating functions
for calculating several of these quantities. Our results also apply to
questions about certain kinds of tilings and rhythm patterns.</description><identifier>DOI: 10.48550/arxiv.1108.0337</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2011-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1108.0337$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1108.0337$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Malandro, Martin E</creatorcontrib><title>Integer compositions with part sizes not exceeding k</title><description>We study the compositions of an integer n whose part sizes do not exceed a
fixed integer k. We use the methods of analytic combinatorics to obtain precise
asymptotic formulas for the number of such compositions, the total number of
parts among all such compositions, the expected number of parts in such a
composition, the total number of times a particular part size appears among all
such compositions, and the expected multiplicity of a given part size in such a
composition. Along the way we also obtain recurrences and generating functions
for calculating several of these quantities. Our results also apply to
questions about certain kinds of tilings and rhythm patterns.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj1vwjAUhWEvDBWwd0L-Awm-sR0nI0J8SUhdskc3zoVahSSyLb5-PdB2OsMrHT2MfYJIVaG1mKO_uUsKIIpUSGk-mNp1kY7kue3PQx9cdH0X-NXFbz6gjzy4BwXe9ZHTzRK1rjvynwkbHfAUaPq_Y1atV9Vym-y_NrvlYp9grk3SCBKZKFGaFg4EjQalINMGS8hlhnmh2lbZXJjslUorNenGAkJhjLGyQTlms7_bX3U9eHdGf6_f-vqtl0_y_z58</recordid><startdate>20110801</startdate><enddate>20110801</enddate><creator>Malandro, Martin E</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20110801</creationdate><title>Integer compositions with part sizes not exceeding k</title><author>Malandro, Martin E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a657-b0e0209a37d1fe1b51441257a91632a684dd4c6072b519c35e5bc1a18777c3ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Malandro, Martin E</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Malandro, Martin E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Integer compositions with part sizes not exceeding k</atitle><date>2011-08-01</date><risdate>2011</risdate><abstract>We study the compositions of an integer n whose part sizes do not exceed a
fixed integer k. We use the methods of analytic combinatorics to obtain precise
asymptotic formulas for the number of such compositions, the total number of
parts among all such compositions, the expected number of parts in such a
composition, the total number of times a particular part size appears among all
such compositions, and the expected multiplicity of a given part size in such a
composition. Along the way we also obtain recurrences and generating functions
for calculating several of these quantities. Our results also apply to
questions about certain kinds of tilings and rhythm patterns.</abstract><doi>10.48550/arxiv.1108.0337</doi><oa>free_for_read</oa></addata></record> |
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| identifier | DOI: 10.48550/arxiv.1108.0337 |
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| source | arXiv.org |
| subjects | Mathematics - Combinatorics |
| title | Integer compositions with part sizes not exceeding k |
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