Last Symbol Distribution in Pattern Avoiding Catalan Words
We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a pattern of length at most three. For each pattern p , we provide a bivariate rational generating function where the coefficient c p ( n , k ) of x n y k in its series expansion is the number of length n C...
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| Veröffentlicht in: | Mathematics in computer science 2024-03, Vol.18 (1), Article 1 |
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| creator | Baril, Jean-Luc González, Javier F. Ramírez, José L. |
| description | We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a pattern of length at most three. For each pattern
p
, we provide a bivariate rational generating function where the coefficient
c
p
(
n
,
k
)
of
x
n
y
k
in its series expansion is the number of length
n
Catalan words avoiding
p
and ending with the symbol
k
. We deduce recurrence relations or closed forms for
c
p
(
n
,
k
)
and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding
p
. We end this paper by describing a computational approach using computer algebra. |
| doi_str_mv | 10.1007/s11786-023-00576-5 |
| format | Article |
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p
, we provide a bivariate rational generating function where the coefficient
c
p
(
n
,
k
)
of
x
n
y
k
in its series expansion is the number of length
n
Catalan words avoiding
p
and ending with the symbol
k
. We deduce recurrence relations or closed forms for
c
p
(
n
,
k
)
and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding
p
. We end this paper by describing a computational approach using computer algebra.</description><identifier>ISSN: 1661-8270</identifier><identifier>EISSN: 1661-8289</identifier><identifier>DOI: 10.1007/s11786-023-00576-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Bivariate analysis ; Computer algebra ; Computer Science ; Mathematics ; Mathematics and Statistics ; Series expansion</subject><ispartof>Mathematics in computer science, 2024-03, Vol.18 (1), Article 1</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-b62355abbbfdfe5189602f1771ffd0b3254efb1356c9bfaba7581cf09f82daeb3</citedby><cites>FETCH-LOGICAL-c363t-b62355abbbfdfe5189602f1771ffd0b3254efb1356c9bfaba7581cf09f82daeb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11786-023-00576-5$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11786-023-00576-5$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Baril, Jean-Luc</creatorcontrib><creatorcontrib>González, Javier F.</creatorcontrib><creatorcontrib>Ramírez, José L.</creatorcontrib><title>Last Symbol Distribution in Pattern Avoiding Catalan Words</title><title>Mathematics in computer science</title><addtitle>Math.Comput.Sci</addtitle><description>We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a pattern of length at most three. For each pattern
p
, we provide a bivariate rational generating function where the coefficient
c
p
(
n
,
k
)
of
x
n
y
k
in its series expansion is the number of length
n
Catalan words avoiding
p
and ending with the symbol
k
. We deduce recurrence relations or closed forms for
c
p
(
n
,
k
)
and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding
p
. We end this paper by describing a computational approach using computer algebra.</description><subject>Bivariate analysis</subject><subject>Computer algebra</subject><subject>Computer Science</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Series expansion</subject><issn>1661-8270</issn><issn>1661-8289</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kMFKAzEURYMoWKs_4CrgOvqSNMmMu1KtCgUFFZchmUnKlDapSSr07x0d0Z2rdxf33AcHoXMKlxRAXWVKVSUJME4AhJJEHKARlZKSilX14W9WcIxOcl4BSEYndISuFyYX_Lzf2LjGN10uqbO70sWAu4CfTCkuBTz9iF3bhSWemWLWJuC3mNp8io68WWd39nPH6HV--zK7J4vHu4fZdEEaLnkhVjIuhLHW-tY7QataAvNUKep9C5YzMXHeUi5kU1tvrFGioo2H2lesNc7yMboYdrcpvu9cLnoVdyn0LzWrmZRQMyb7FhtaTYo5J-f1NnUbk_aagv5ypAdHunekvx1p0UN8gHJfDkuX_qb_oT4BQydpnQ</recordid><startdate>20240301</startdate><enddate>20240301</enddate><creator>Baril, Jean-Luc</creator><creator>González, Javier F.</creator><creator>Ramírez, José L.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240301</creationdate><title>Last Symbol Distribution in Pattern Avoiding Catalan Words</title><author>Baril, Jean-Luc ; González, Javier F. ; Ramírez, José L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-b62355abbbfdfe5189602f1771ffd0b3254efb1356c9bfaba7581cf09f82daeb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Bivariate analysis</topic><topic>Computer algebra</topic><topic>Computer Science</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Series expansion</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Baril, Jean-Luc</creatorcontrib><creatorcontrib>González, Javier F.</creatorcontrib><creatorcontrib>Ramírez, José L.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Mathematics in computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Baril, Jean-Luc</au><au>González, Javier F.</au><au>Ramírez, José L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Last Symbol Distribution in Pattern Avoiding Catalan Words</atitle><jtitle>Mathematics in computer science</jtitle><stitle>Math.Comput.Sci</stitle><date>2024-03-01</date><risdate>2024</risdate><volume>18</volume><issue>1</issue><artnum>1</artnum><issn>1661-8270</issn><eissn>1661-8289</eissn><abstract>We study the distribution of the last symbol statistics on the sets of Catalan words avoiding a pattern of length at most three. For each pattern
p
, we provide a bivariate rational generating function where the coefficient
c
p
(
n
,
k
)
of
x
n
y
k
in its series expansion is the number of length
n
Catalan words avoiding
p
and ending with the symbol
k
. We deduce recurrence relations or closed forms for
c
p
(
n
,
k
)
and we provide asymptotic approximations for the expectation of the last symbol on all Catalan words avoiding
p
. We end this paper by describing a computational approach using computer algebra.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11786-023-00576-5</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1661-8270 |
| ispartof | Mathematics in computer science, 2024-03, Vol.18 (1), Article 1 |
| issn | 1661-8270 1661-8289 |
| language | eng |
| recordid | cdi_proquest_journals_2926609226 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Bivariate analysis Computer algebra Computer Science Mathematics Mathematics and Statistics Series expansion |
| title | Last Symbol Distribution in Pattern Avoiding Catalan Words |
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