On congruence schemes for constant terms and their applications
Rowland and Zeilberger devised an approach to algorithmically determine the modulo p r reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting p -schemes are systems of recurrences and, depending on their shape, are cla...
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| Veröffentlicht in: | Research in number theory 2022-09, Vol.8 (3), Article 42 |
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| container_title | Research in number theory |
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| creator | Straub, Armin |
| description | Rowland and Zeilberger devised an approach to algorithmically determine the modulo
p
r
reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting
p
-schemes are systems of recurrences and, depending on their shape, are classified as automatic or linear. We revisit this approach, provide some additional details such as bounding the number of states, and suggest a third natural type of scheme that combines benefits of automatic and linear ones. We illustrate the utility of these “scaling” schemes by confirming and extending a conjecture of Rowland and Yassawi on Motzkin numbers. |
| doi_str_mv | 10.1007/s40993-022-00337-6 |
| format | Article |
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p
r
reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting
p
-schemes are systems of recurrences and, depending on their shape, are classified as automatic or linear. We revisit this approach, provide some additional details such as bounding the number of states, and suggest a third natural type of scheme that combines benefits of automatic and linear ones. We illustrate the utility of these “scaling” schemes by confirming and extending a conjecture of Rowland and Yassawi on Motzkin numbers.</description><identifier>ISSN: 2522-0160</identifier><identifier>EISSN: 2363-9555</identifier><identifier>DOI: 10.1007/s40993-022-00337-6</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Combinatorial analysis ; Mathematics ; Mathematics and Statistics ; Number Theory</subject><ispartof>Research in number theory, 2022-09, Vol.8 (3), Article 42</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-937d317a9a8260ffb37361fdbad2e70342bd3000a654bfac70873143ec77a3f03</citedby><cites>FETCH-LOGICAL-c249t-937d317a9a8260ffb37361fdbad2e70342bd3000a654bfac70873143ec77a3f03</cites><orcidid>0000-0001-6802-6053</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40993-022-00337-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40993-022-00337-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27907,27908,41471,42540,51302</link.rule.ids></links><search><creatorcontrib>Straub, Armin</creatorcontrib><title>On congruence schemes for constant terms and their applications</title><title>Research in number theory</title><addtitle>Res. number theory</addtitle><description>Rowland and Zeilberger devised an approach to algorithmically determine the modulo
p
r
reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting
p
-schemes are systems of recurrences and, depending on their shape, are classified as automatic or linear. We revisit this approach, provide some additional details such as bounding the number of states, and suggest a third natural type of scheme that combines benefits of automatic and linear ones. We illustrate the utility of these “scaling” schemes by confirming and extending a conjecture of Rowland and Yassawi on Motzkin numbers.</description><subject>Combinatorial analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><issn>2522-0160</issn><issn>2363-9555</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LAzEUDKJg0f4BTwHP0Ze83aR7Eil-QaEXPYdsNmm3tNk1SQ_-e1NX8ObpDe_NzBuGkBsOdxxA3acKmgYZCMEAEBWTZ2QmUCJr6ro-L7g-nbiESzJPaQdQMFZCiBl5WAdqh7CJRxeso8lu3cEl6od4WqdsQqbZxUOiJnQ0b10fqRnHfW9N7gvhmlx4s09u_juvyMfz0_vyla3WL2_LxxWzomoya1B1yJVpzEJI8L5FhZL7rjWdcApKmLbDksvIumq9sQoWCnmFzipl0ANekdvJd4zD59GlrHfDMYbyUgu5QF6LYl9YYmLZOKQUnddj7A8mfmkO-tSVnrrSpSv905WWRYSTKBVy2Lj4Z_2P6hs1xWsq</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Straub, Armin</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-6802-6053</orcidid></search><sort><creationdate>20220901</creationdate><title>On congruence schemes for constant terms and their applications</title><author>Straub, Armin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-937d317a9a8260ffb37361fdbad2e70342bd3000a654bfac70873143ec77a3f03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Combinatorial analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Straub, Armin</creatorcontrib><collection>CrossRef</collection><jtitle>Research in number theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Straub, Armin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On congruence schemes for constant terms and their applications</atitle><jtitle>Research in number theory</jtitle><stitle>Res. number theory</stitle><date>2022-09-01</date><risdate>2022</risdate><volume>8</volume><issue>3</issue><artnum>42</artnum><issn>2522-0160</issn><eissn>2363-9555</eissn><abstract>Rowland and Zeilberger devised an approach to algorithmically determine the modulo
p
r
reductions of values of combinatorial sequences representable as constant terms (building on work of Rowland and Yassawi). The resulting
p
-schemes are systems of recurrences and, depending on their shape, are classified as automatic or linear. We revisit this approach, provide some additional details such as bounding the number of states, and suggest a third natural type of scheme that combines benefits of automatic and linear ones. We illustrate the utility of these “scaling” schemes by confirming and extending a conjecture of Rowland and Yassawi on Motzkin numbers.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40993-022-00337-6</doi><orcidid>https://orcid.org/0000-0001-6802-6053</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | Research in number theory, 2022-09, Vol.8 (3), Article 42 |
| issn | 2522-0160 2363-9555 |
| language | eng |
| recordid | cdi_proquest_journals_2683152317 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Combinatorial analysis Mathematics Mathematics and Statistics Number Theory |
| title | On congruence schemes for constant terms and their applications |
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