The k -Extensions of some New Mahonian Statistics
Identifieur interne : 000299 ( Istex/Curation ); précédent : 000298; suivant : 000300The k -Extensions of some New Mahonian Statistics
Auteurs : Robert J. Clarke ; Einar Steingr Amp X0301 Msson [Suède] ; Jiang Zeng [France]Source :
- European Journal of Combinatorics [ 0195-6698 ] ; 1997.
English descriptors
- KwdEn :
- Bijection, Clarke, Corresponding column, Denk, Descent bottom, Descent bottoms, Descent tops, Desk madk makk, Ebotk, Envk, Excedance, Excedance place, Excedance places, Excedance tops, Excedances, Exck, Exck invk denk, Fraction expansion, Imvk, Invk, Jiang zeng, Large letters, Madk, Mahonian, Mahonian statistics, Makk, Permutation, Side numbers, Symmetric group.
- Teeft :
- Bijection, Clarke, Corresponding column, Denk, Descent bottom, Descent bottoms, Descent tops, Desk madk makk, Ebotk, Envk, Excedance, Excedance place, Excedance places, Excedance tops, Excedances, Exck, Exck invk denk, Fraction expansion, Imvk, Invk, Jiang zeng, Large letters, Madk, Mahonian, Mahonian statistics, Makk, Permutation, Side numbers, Symmetric group.
Abstract
Abstract: In previous work by the authors, new Mahonian statistics ENV, MAD and MAK were defined on words, and it was shown that ENV is equal to the classical statistic INV and that the triple statistics (des, MAK, MAD) and (exc, DEN, ENV) are equidistributed over any rearrangement class of words. Here, exc and des are the classical Eulerian statistics, while DEN is Denert's statistic. In addition, a bijection between the symmetric group and sets of weighted Motzkin paths was used to give a continued fraction expression for the generating function of (exc, INV) or (des, MAD) on the symmetric group. These results are extended to the case in which the letters of the alphabet used are divided into two classes—large and small—with corresponding changes to the definitions of the above statistics.
Url:
DOI: 10.1006/eujc.1996.0088
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Robert J. Clarke<affiliation><mods:affiliation>Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia, 5005</mods:affiliation><wicri:noCountry code="subField">5005</wicri:noCountry></affiliation>Le document en format XML
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Clarke</name><affiliation><mods:affiliation>Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia, 5005</mods:affiliation><wicri:noCountry code="subField">5005</wicri:noCountry></affiliation></author><author><name sortKey="Steingr Amp X0301 Msson, Einar" sort="Steingr Amp X0301 Msson, Einar" uniqKey="Steingr Amp X0301 Msson E" first="Einar" last="Steingr Amp X0301 Msson">Einar Steingr Amp X0301 Msson</name><affiliation wicri:level="1"><mods:affiliation>Matematiska institutionen, CTH & GU, 412 96 Göteborg, Sweden</mods:affiliation><country xml:lang="fr">Suède</country><wicri:regionArea>Matematiska institutionen, CTH & GU, 412 96 Göteborg</wicri:regionArea></affiliation></author><author><name sortKey="Zeng, Jiang" sort="Zeng, Jiang" uniqKey="Zeng J" first="Jiang" last="Zeng">Jiang Zeng</name><affiliation wicri:level="1"><mods:affiliation>Département de mathématique, Université Louis-Pasteur, 67084 Strasbourg Cedex, France</mods:affiliation><country xml:lang="fr">France</country><wicri:regionArea>Département de mathématique, Université Louis-Pasteur, 67084 Strasbourg Cedex</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:0F702B87A51711285876A500EA5520A2E505D0D1</idno><date when="1997" year="1997">1997</date><idno type="doi">10.1006/eujc.1996.0088</idno><idno type="url">https://api.istex.fr/document/0F702B87A51711285876A500EA5520A2E505D0D1/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000299</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000299</idno><idno type="wicri:Area/Istex/Curation">000299</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">The k -Extensions of some New Mahonian Statistics</title><author><name sortKey="Clarke, Robert J" sort="Clarke, Robert J" uniqKey="Clarke R" first="Robert J." last="Clarke">Robert J. Clarke</name><affiliation><mods:affiliation>Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia, 5005</mods:affiliation><wicri:noCountry code="subField">5005</wicri:noCountry></affiliation></author><author><name sortKey="Steingr Amp X0301 Msson, Einar" sort="Steingr Amp X0301 Msson, Einar" uniqKey="Steingr Amp X0301 Msson E" first="Einar" last="Steingr Amp X0301 Msson">Einar Steingr Amp X0301 Msson</name><affiliation wicri:level="1"><mods:affiliation>Matematiska institutionen, CTH & GU, 412 96 Göteborg, Sweden</mods:affiliation><country xml:lang="fr">Suède</country><wicri:regionArea>Matematiska institutionen, CTH & GU, 412 96 Göteborg</wicri:regionArea></affiliation></author><author><name sortKey="Zeng, Jiang" sort="Zeng, Jiang" uniqKey="Zeng J" first="Jiang" last="Zeng">Jiang Zeng</name><affiliation wicri:level="1"><mods:affiliation>Département de mathématique, Université Louis-Pasteur, 67084 Strasbourg Cedex, France</mods:affiliation><country xml:lang="fr">France</country><wicri:regionArea>Département de mathématique, Université Louis-Pasteur, 67084 Strasbourg Cedex</wicri:regionArea></affiliation></author></analytic><monogr></monogr><series><title level="j">European Journal of Combinatorics</title><title level="j" type="abbrev">YEUJC</title><idno type="ISSN">0195-6698</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1997">1997</date><biblScope unit="volume">18</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="143">143</biblScope><biblScope unit="page" to="154">154</biblScope></imprint><idno type="ISSN">0195-6698</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0195-6698</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Bijection</term><term>Clarke</term><term>Corresponding column</term><term>Denk</term><term>Descent bottom</term><term>Descent bottoms</term><term>Descent tops</term><term>Desk madk makk</term><term>Ebotk</term><term>Envk</term><term>Excedance</term><term>Excedance place</term><term>Excedance places</term><term>Excedance tops</term><term>Excedances</term><term>Exck</term><term>Exck invk denk</term><term>Fraction expansion</term><term>Imvk</term><term>Invk</term><term>Jiang zeng</term><term>Large letters</term><term>Madk</term><term>Mahonian</term><term>Mahonian statistics</term><term>Makk</term><term>Permutation</term><term>Side numbers</term><term>Symmetric group</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Bijection</term><term>Clarke</term><term>Corresponding column</term><term>Denk</term><term>Descent bottom</term><term>Descent bottoms</term><term>Descent tops</term><term>Desk madk makk</term><term>Ebotk</term><term>Envk</term><term>Excedance</term><term>Excedance place</term><term>Excedance places</term><term>Excedance tops</term><term>Excedances</term><term>Exck</term><term>Exck invk denk</term><term>Fraction expansion</term><term>Imvk</term><term>Invk</term><term>Jiang zeng</term><term>Large letters</term><term>Madk</term><term>Mahonian</term><term>Mahonian statistics</term><term>Makk</term><term>Permutation</term><term>Side numbers</term><term>Symmetric group</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: In previous work by the authors, new Mahonian statistics ENV, MAD and MAK were defined on words, and it was shown that ENV is equal to the classical statistic INV and that the triple statistics (des, MAK, MAD) and (exc, DEN, ENV) are equidistributed over any rearrangement class of words. Here, exc and des are the classical Eulerian statistics, while DEN is Denert's statistic. In addition, a bijection between the symmetric group and sets of weighted Motzkin paths was used to give a continued fraction expression for the generating function of (exc, INV) or (des, MAD) on the symmetric group. These results are extended to the case in which the letters of the alphabet used are divided into two classes—large and small—with corresponding changes to the definitions of the above statistics.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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