Turán inequalities for the broken k-diamond partition functions
We obtain an asymptotic formula for Andrews and Paule’s broken k -diamond partition function Δ k ( n ) , where k = 1 or 2. Based on this asymptotic formula, we derive that Δ k ( n ) satisfies the order d Turán inequalities for d ≥ 1 and for sufficiently large n when k = 1 or 2 by using a general res...
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| Veröffentlicht in: | The Ramanujan journal 2023-10, Vol.62 (2), p.593-615 |
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| creator | Dong, Janet J. W. Ji, Kathy Q. Jia, Dennis X. Q. |
| description | We obtain an asymptotic formula for Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
, where
k
=
1
or 2. Based on this asymptotic formula, we derive that
Δ
k
(
n
)
satisfies the order
d
Turán inequalities for
d
≥
1
and for sufficiently large
n
when
k
=
1
or 2 by using a general result of Griffin, Ono, Rolen, and Zagier. We also show that Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
is log-concave for
n
≥
1
when
k
=
1
or 2, which implies that
Δ
k
(
a
)
Δ
k
(
b
)
≥
Δ
k
(
a
+
b
)
for
a
,
b
≥
1
when
k
=
1
or 2. |
| doi_str_mv | 10.1007/s11139-022-00687-w |
| format | Article |
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k
-diamond partition function
Δ
k
(
n
)
, where
k
=
1
or 2. Based on this asymptotic formula, we derive that
Δ
k
(
n
)
satisfies the order
d
Turán inequalities for
d
≥
1
and for sufficiently large
n
when
k
=
1
or 2 by using a general result of Griffin, Ono, Rolen, and Zagier. We also show that Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
is log-concave for
n
≥
1
when
k
=
1
or 2, which implies that
Δ
k
(
a
)
Δ
k
(
b
)
≥
Δ
k
(
a
+
b
)
for
a
,
b
≥
1
when
k
=
1
or 2.</description><identifier>ISSN: 1382-4090</identifier><identifier>EISSN: 1572-9303</identifier><identifier>DOI: 10.1007/s11139-022-00687-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Asymptotic properties ; Combinatorics ; Diamonds ; Field Theory and Polynomials ; Fourier Analysis ; Functions of a Complex Variable ; Inequalities ; Mathematics ; Mathematics and Statistics ; Number Theory ; Partitions (mathematics)</subject><ispartof>The Ramanujan journal, 2023-10, Vol.62 (2), p.593-615</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-d76b59f566bc951871ec09eec580c599b18058142404ba15ce623076fc43f9093</citedby><cites>FETCH-LOGICAL-c319t-d76b59f566bc951871ec09eec580c599b18058142404ba15ce623076fc43f9093</cites><orcidid>0000-0001-8792-2531</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/s11139-022-00687-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11139-022-00687-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Dong, Janet J. W.</creatorcontrib><creatorcontrib>Ji, Kathy Q.</creatorcontrib><creatorcontrib>Jia, Dennis X. Q.</creatorcontrib><title>Turán inequalities for the broken k-diamond partition functions</title><title>The Ramanujan journal</title><addtitle>Ramanujan J</addtitle><description>We obtain an asymptotic formula for Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
, where
k
=
1
or 2. Based on this asymptotic formula, we derive that
Δ
k
(
n
)
satisfies the order
d
Turán inequalities for
d
≥
1
and for sufficiently large
n
when
k
=
1
or 2 by using a general result of Griffin, Ono, Rolen, and Zagier. We also show that Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
is log-concave for
n
≥
1
when
k
=
1
or 2, which implies that
Δ
k
(
a
)
Δ
k
(
b
)
≥
Δ
k
(
a
+
b
)
for
a
,
b
≥
1
when
k
=
1
or 2.</description><subject>Asymptotic properties</subject><subject>Combinatorics</subject><subject>Diamonds</subject><subject>Field Theory and Polynomials</subject><subject>Fourier Analysis</subject><subject>Functions of a Complex Variable</subject><subject>Inequalities</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Partitions (mathematics)</subject><issn>1382-4090</issn><issn>1572-9303</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kEtOwzAURS0EEqWwAUaRGBue__EMVPGTKjEpYytxbEg_TmsnqlgOa2FjuASJGaN3B-fcJ12ELglcEwB1kwghTGOgFAPIUuH9EZoQoSjWDNhxzqykmIOGU3SW0hIAODA1QbeLIX59hqINbjdU67ZvXSp8F4v-3RV17FYuFCvctNWmC02xrWKfkS4Ufgj2ENI5OvHVOrmL3ztFrw_3i9kTnr88Ps_u5tgyonvcKFkL7YWUtdWClIo4C9o5K0qwQuualCBKwikHXldEWCcpAyW95cxr0GyKrsbebex2g0u9WXZDDPmloaUUItv8QNGRsrFLKTpvtrHdVPHDEDCHpcy4lMlLmZ-lzD5LbJRShsObi3_V_1jf1j5r8g</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Dong, Janet J. W.</creator><creator>Ji, Kathy Q.</creator><creator>Jia, Dennis X. Q.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-8792-2531</orcidid></search><sort><creationdate>20231001</creationdate><title>Turán inequalities for the broken k-diamond partition functions</title><author>Dong, Janet J. W. ; Ji, Kathy Q. ; Jia, Dennis X. Q.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-d76b59f566bc951871ec09eec580c599b18058142404ba15ce623076fc43f9093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Asymptotic properties</topic><topic>Combinatorics</topic><topic>Diamonds</topic><topic>Field Theory and Polynomials</topic><topic>Fourier Analysis</topic><topic>Functions of a Complex Variable</topic><topic>Inequalities</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Partitions (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dong, Janet J. W.</creatorcontrib><creatorcontrib>Ji, Kathy Q.</creatorcontrib><creatorcontrib>Jia, Dennis X. Q.</creatorcontrib><collection>CrossRef</collection><jtitle>The Ramanujan journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dong, Janet J. W.</au><au>Ji, Kathy Q.</au><au>Jia, Dennis X. Q.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Turán inequalities for the broken k-diamond partition functions</atitle><jtitle>The Ramanujan journal</jtitle><stitle>Ramanujan J</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>62</volume><issue>2</issue><spage>593</spage><epage>615</epage><pages>593-615</pages><issn>1382-4090</issn><eissn>1572-9303</eissn><abstract>We obtain an asymptotic formula for Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
, where
k
=
1
or 2. Based on this asymptotic formula, we derive that
Δ
k
(
n
)
satisfies the order
d
Turán inequalities for
d
≥
1
and for sufficiently large
n
when
k
=
1
or 2 by using a general result of Griffin, Ono, Rolen, and Zagier. We also show that Andrews and Paule’s broken
k
-diamond partition function
Δ
k
(
n
)
is log-concave for
n
≥
1
when
k
=
1
or 2, which implies that
Δ
k
(
a
)
Δ
k
(
b
)
≥
Δ
k
(
a
+
b
)
for
a
,
b
≥
1
when
k
=
1
or 2.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11139-022-00687-w</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0001-8792-2531</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1382-4090 |
| ispartof | The Ramanujan journal, 2023-10, Vol.62 (2), p.593-615 |
| issn | 1382-4090 1572-9303 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Asymptotic properties Combinatorics Diamonds Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Inequalities Mathematics Mathematics and Statistics Number Theory Partitions (mathematics) |
| title | Turán inequalities for the broken k-diamond partition functions |
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