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Common substring with shifts in b-ary expansions
Denote by S n ( x , y ) the length of the longest common substring of x and y with shifts in their first n digits of the b -ary expansions. We show that the sets of pairs ( x , y ), for which the growth rate of S n ( x , y ) is α log n with 0 ≤ α ≤ ∞ , have full Hausdorff dimension. Our method reli...
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| Published in: | Archiv der Mathematik 2024-10, Vol.123 (4), p.369-377 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| cites | cdi_FETCH-LOGICAL-c200t-c9206eeef4aeafcc06d7c750c6577ba6584d741506166a29aa97ea32899a6be23 |
| container_end_page | 377 |
| container_issue | 4 |
| container_start_page | 369 |
| container_title | Archiv der Mathematik |
| container_volume | 123 |
| creator | Liao, Xin Yu, Dingding |
| description | Denote by
S
n
(
x
,
y
)
the length of the longest common substring of
x
and
y
with shifts in their first
n
digits of the
b
-ary expansions. We show that the sets of pairs (
x
,
y
), for which the growth rate of
S
n
(
x
,
y
)
is
α
log
n
with
0
≤
α
≤
∞
, have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices. |
| doi_str_mv | 10.1007/s00013-024-02038-1 |
| format | article |
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S
n
(
x
,
y
)
the length of the longest common substring of
x
and
y
with shifts in their first
n
digits of the
b
-ary expansions. We show that the sets of pairs (
x
,
y
), for which the growth rate of
S
n
(
x
,
y
)
is
α
log
n
with
0
≤
α
≤
∞
, have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices.</description><identifier>ISSN: 0003-889X</identifier><identifier>EISSN: 1420-8938</identifier><identifier>DOI: 10.1007/s00013-024-02038-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Archiv der Mathematik, 2024-10, Vol.123 (4), p.369-377</ispartof><rights>Springer Nature Switzerland AG 2024. 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><cites>FETCH-LOGICAL-c200t-c9206eeef4aeafcc06d7c750c6577ba6584d741506166a29aa97ea32899a6be23</cites><orcidid>0009-0009-7111-6872</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Liao, Xin</creatorcontrib><creatorcontrib>Yu, Dingding</creatorcontrib><title>Common substring with shifts in b-ary expansions</title><title>Archiv der Mathematik</title><addtitle>Arch. Math</addtitle><description>Denote by
S
n
(
x
,
y
)
the length of the longest common substring of
x
and
y
with shifts in their first
n
digits of the
b
-ary expansions. We show that the sets of pairs (
x
,
y
), for which the growth rate of
S
n
(
x
,
y
)
is
α
log
n
with
0
≤
α
≤
∞
, have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0003-889X</issn><issn>1420-8938</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AU8Fz9HJR_NxlOIXLHhR8BbSbOp2cduaaVH_vVkrePMwzGHe952Zh5BzBpcMQF8hADBBgctcIAxlB2TBJAdqrDCHZJHnghpjX47JCeI2q7nRdkGg6ne7vitwqnFMbfdafLTjpsBN24xYtF1RU5--ivg5-A7bvsNTctT4N4xnv31Jnm9vnqp7unq8e6iuVzRwgJEGy0HFGBvpo29CALXWQZcQVKl17VVp5FpLVoJiSnluvbc6esGNtV7VkYsluZhzh9S_TxFHt-2n1OWVTjAmpZFK6qzisyqkHjHFxg2p3eWLHQO3J-NmMi6TcT9kHMsmMZtw2H8c01_0P65vVg1lQg</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Liao, Xin</creator><creator>Yu, Dingding</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0009-0009-7111-6872</orcidid></search><sort><creationdate>20241001</creationdate><title>Common substring with shifts in b-ary expansions</title><author>Liao, Xin ; Yu, Dingding</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-c9206eeef4aeafcc06d7c750c6577ba6584d741506166a29aa97ea32899a6be23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liao, Xin</creatorcontrib><creatorcontrib>Yu, Dingding</creatorcontrib><collection>CrossRef</collection><jtitle>Archiv der Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liao, Xin</au><au>Yu, Dingding</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Common substring with shifts in b-ary expansions</atitle><jtitle>Archiv der Mathematik</jtitle><stitle>Arch. Math</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>123</volume><issue>4</issue><spage>369</spage><epage>377</epage><pages>369-377</pages><issn>0003-889X</issn><eissn>1420-8938</eissn><abstract>Denote by
S
n
(
x
,
y
)
the length of the longest common substring of
x
and
y
with shifts in their first
n
digits of the
b
-ary expansions. We show that the sets of pairs (
x
,
y
), for which the growth rate of
S
n
(
x
,
y
)
is
α
log
n
with
0
≤
α
≤
∞
, have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00013-024-02038-1</doi><tpages>9</tpages><orcidid>https://orcid.org/0009-0009-7111-6872</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-889X |
| ispartof | Archiv der Mathematik, 2024-10, Vol.123 (4), p.369-377 |
| issn | 0003-889X 1420-8938 |
| language | eng |
| recordid | cdi_proquest_journals_3114484647 |
| source | Springer Link |
| subjects | Mathematics Mathematics and Statistics |
| title | Common substring with shifts in b-ary expansions |
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