Some Elementary Partition Inequalities and Their Implications
Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions wit...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Berkovich, Alexander [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
Partitions with bounded differences between largest and smallest parts |
|---|
| Anmerkung: |
© The Author(s) 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of combinatorics - Springer International Publishing, 1997, 23(2019), 2 vom: 14. Mai, Seite 263-284 |
|---|---|
| Übergeordnetes Werk: |
volume:23 ; year:2019 ; number:2 ; day:14 ; month:05 ; pages:263-284 |
| Links: |
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| DOI / URN: |
10.1007/s00026-019-00433-y |
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OLC2061537022 |
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| 520 | |a Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. Here l and s are the largest part and the smallest part of the partition, respectively. | ||
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10.1007/s00026-019-00433-y doi (DE-627)OLC2061537022 (DE-He213)s00026-019-00433-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berkovich, Alexander verfasserin aut Some Elementary Partition Inequalities and Their Implications 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. Here l and s are the largest part and the smallest part of the partition, respectively. Partition inequalities Partitions with bounded differences between largest and smallest parts Non-negative -series expansions Injective maps -Binomial theorem Heine transformations Jackson transformation Uncu, Ali Kemal aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 23(2019), 2 vom: 14. Mai, Seite 263-284 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:23 year:2019 number:2 day:14 month:05 pages:263-284 https://doi.org/10.1007/s00026-019-00433-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 AR 23 2019 2 14 05 263-284 |
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10.1007/s00026-019-00433-y doi (DE-627)OLC2061537022 (DE-He213)s00026-019-00433-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berkovich, Alexander verfasserin aut Some Elementary Partition Inequalities and Their Implications 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. Here l and s are the largest part and the smallest part of the partition, respectively. Partition inequalities Partitions with bounded differences between largest and smallest parts Non-negative -series expansions Injective maps -Binomial theorem Heine transformations Jackson transformation Uncu, Ali Kemal aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 23(2019), 2 vom: 14. Mai, Seite 263-284 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:23 year:2019 number:2 day:14 month:05 pages:263-284 https://doi.org/10.1007/s00026-019-00433-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 AR 23 2019 2 14 05 263-284 |
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Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. Here l and s are the largest part and the smallest part of the partition, respectively. © The Author(s) 2019 |
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Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. Here l and s are the largest part and the smallest part of the partition, respectively. © The Author(s) 2019 |
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Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. Here l and s are the largest part and the smallest part of the partition, respectively. © The Author(s) 2019 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2061537022</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230323113657.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2019 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00026-019-00433-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2061537022</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00026-019-00433-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Berkovich, Alexander</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Some Elementary Partition Inequalities and Their Implications</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequences of these partition inequalities. In particular, we show that for $$L\ge 1$$, the number of partitions with $$l-s \le L$$ and $$s=1$$ is greater than the number of partitions with $$l-s\le L$$ and $$s>1$$. 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