On longest increasing subsequences in words in which all multiplicities are equal
Journal of Integer Sequences, Vol. 26 (2023), Article 23.7.3 Gessel's famous Bessel determinant formula gives the generating function of the number of permutations without increasing subsequences of a given length. Ekhad and Zeilberger proposed the challenge of finding a suitable generalization...
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| description | Journal of Integer Sequences, Vol. 26 (2023), Article 23.7.3 Gessel's famous Bessel determinant formula gives the generating function of
the number of permutations without increasing subsequences of a given length.
Ekhad and Zeilberger proposed the challenge of finding a suitable
generalization for permutations of multisets in which all multiplicities are
equal, that is, to count words of length $rn$ from an alphabet consisting of
$n$ letters in which each letter appears exactly $r$ times and which have no
increasing subsequences of length $d$.
In this paper we present such a generating function expressible as a multiple
integral of the product of a Gessel-type Toeplitz determinant with the
exponentiated cycle index polynomial of the symmetric group on $r$ elements. |
| doi_str_mv | 10.48550/arxiv.1505.01389 |
| format | Article |
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the number of permutations without increasing subsequences of a given length.
Ekhad and Zeilberger proposed the challenge of finding a suitable
generalization for permutations of multisets in which all multiplicities are
equal, that is, to count words of length $rn$ from an alphabet consisting of
$n$ letters in which each letter appears exactly $r$ times and which have no
increasing subsequences of length $d$.
In this paper we present such a generating function expressible as a multiple
integral of the product of a Gessel-type Toeplitz determinant with the
exponentiated cycle index polynomial of the symmetric group on $r$ elements.</description><identifier>DOI: 10.48550/arxiv.1505.01389</identifier><language>eng</language><subject>Mathematics - Combinatorics ; Mathematics - Probability</subject><creationdate>2015-05</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/1505.01389$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1505.01389$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Balogh, Ferenc</creatorcontrib><title>On longest increasing subsequences in words in which all multiplicities are equal</title><description>Journal of Integer Sequences, Vol. 26 (2023), Article 23.7.3 Gessel's famous Bessel determinant formula gives the generating function of
the number of permutations without increasing subsequences of a given length.
Ekhad and Zeilberger proposed the challenge of finding a suitable
generalization for permutations of multisets in which all multiplicities are
equal, that is, to count words of length $rn$ from an alphabet consisting of
$n$ letters in which each letter appears exactly $r$ times and which have no
increasing subsequences of length $d$.
In this paper we present such a generating function expressible as a multiple
integral of the product of a Gessel-type Toeplitz determinant with the
exponentiated cycle index polynomial of the symmetric group on $r$ elements.</description><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8luAjEQRH3JIYJ8QE7xD8zES2w8R4SySUgIifuop22DJWOIPZPl7-NA-tKtqq6SHiH3nLVPRin2CPk7fLZcMdUyLk13S7abROMp7V0ZaUiYHZSQ9rRMQ3Efk0voStXp1ynb63EIeKAQIz1OcQznGDCMoT5BdrQmIM7JjYdY3N3_npHdy_Nu9dasN6_vq-W6Ab3oGkBQjCFIZ00dPaDi1gvZCW2YdloazzpgotpWe2vADx0KjmiEHMQC5Yw8XGsvTP05hyPkn_6Prb-wyV87JUsu</recordid><startdate>20150506</startdate><enddate>20150506</enddate><creator>Balogh, Ferenc</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20150506</creationdate><title>On longest increasing subsequences in words in which all multiplicities are equal</title><author>Balogh, Ferenc</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-aca500ca3ed88886bc51df23926806e638f09a02ed8d6fd8afb9c21cc823b27c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Balogh, Ferenc</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Balogh, Ferenc</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On longest increasing subsequences in words in which all multiplicities are equal</atitle><date>2015-05-06</date><risdate>2015</risdate><abstract>Journal of Integer Sequences, Vol. 26 (2023), Article 23.7.3 Gessel's famous Bessel determinant formula gives the generating function of
the number of permutations without increasing subsequences of a given length.
Ekhad and Zeilberger proposed the challenge of finding a suitable
generalization for permutations of multisets in which all multiplicities are
equal, that is, to count words of length $rn$ from an alphabet consisting of
$n$ letters in which each letter appears exactly $r$ times and which have no
increasing subsequences of length $d$.
In this paper we present such a generating function expressible as a multiple
integral of the product of a Gessel-type Toeplitz determinant with the
exponentiated cycle index polynomial of the symmetric group on $r$ elements.</abstract><doi>10.48550/arxiv.1505.01389</doi><oa>free_for_read</oa></addata></record> |
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| title | On longest increasing subsequences in words in which all multiplicities are equal |
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