Combinatorial Interpretations of Convolutions of the Catalan Numbers
We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Tedford, Steven J. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Walter de Gruyter GmbH & Co. KG ; 2011 |
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| Schlagwörter: |
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| Anmerkung: |
© de Gruyter 2011 |
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| Umfang: |
11 |
| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
In: 11(2011), 1 vom: 24. Feb., Seite 35-45 volume:11 ; year:2011 ; number:1 ; day:24 ; month:02 ; pages:35-45 ; extent:11 |
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| DOI / URN: |
10.1515/integ.2011.003 |
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| 520 | |a We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. | ||
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10.1515/integ.2011.003 doi artikel_Grundlieferung.pp (DE-627)NLEJ247026506 DE-627 ger DE-627 rakwb Tedford, Steven J. verfasserin aut Combinatorial Interpretations of Convolutions of the Catalan Numbers Walter de Gruyter GmbH & Co. KG 2011 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. Walter de Gruyter Online Zeitschriften Catalan Numbers convolutions Pascal's Triangle In 11(2011), 1 vom: 24. Feb., Seite 35-45 volume:11 year:2011 number:1 day:24 month:02 pages:35-45 extent:11 https://doi.org/10.1515/integ.2011.003 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 1 24 02 35-45 11 |
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10.1515/integ.2011.003 doi artikel_Grundlieferung.pp (DE-627)NLEJ247026506 DE-627 ger DE-627 rakwb Tedford, Steven J. verfasserin aut Combinatorial Interpretations of Convolutions of the Catalan Numbers Walter de Gruyter GmbH & Co. KG 2011 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. Walter de Gruyter Online Zeitschriften Catalan Numbers convolutions Pascal's Triangle In 11(2011), 1 vom: 24. Feb., Seite 35-45 volume:11 year:2011 number:1 day:24 month:02 pages:35-45 extent:11 https://doi.org/10.1515/integ.2011.003 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 1 24 02 35-45 11 |
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10.1515/integ.2011.003 doi artikel_Grundlieferung.pp (DE-627)NLEJ247026506 DE-627 ger DE-627 rakwb Tedford, Steven J. verfasserin aut Combinatorial Interpretations of Convolutions of the Catalan Numbers Walter de Gruyter GmbH & Co. KG 2011 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. Walter de Gruyter Online Zeitschriften Catalan Numbers convolutions Pascal's Triangle In 11(2011), 1 vom: 24. Feb., Seite 35-45 volume:11 year:2011 number:1 day:24 month:02 pages:35-45 extent:11 https://doi.org/10.1515/integ.2011.003 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 1 24 02 35-45 11 |
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10.1515/integ.2011.003 doi artikel_Grundlieferung.pp (DE-627)NLEJ247026506 DE-627 ger DE-627 rakwb Tedford, Steven J. verfasserin aut Combinatorial Interpretations of Convolutions of the Catalan Numbers Walter de Gruyter GmbH & Co. KG 2011 11 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. Walter de Gruyter Online Zeitschriften Catalan Numbers convolutions Pascal's Triangle In 11(2011), 1 vom: 24. Feb., Seite 35-45 volume:11 year:2011 number:1 day:24 month:02 pages:35-45 extent:11 https://doi.org/10.1515/integ.2011.003 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 1 24 02 35-45 11 |
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Combinatorial Interpretations of Convolutions of the Catalan Numbers |
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We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. © de Gruyter 2011 |
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We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. © de Gruyter 2011 |
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We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle. © de Gruyter 2011 |
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