Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices
Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. Thes...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kim, T. [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Russian journal of mathematical physics - Pleiades Publishing, 1993, 29(2022), 3 vom: Sept., Seite 358-377 |
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| Übergeordnetes Werk: |
volume:29 ; year:2022 ; number:3 ; month:09 ; pages:358-377 |
| Links: |
|---|
| DOI / URN: |
10.1134/S1061920822030050 |
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OLC2131964269 |
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| 520 | |a Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. | ||
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10.1134/S1061920822030050 doi (DE-627)OLC2131964269 (DE-He213)S1061920822030050-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kim, T. verfasserin aut Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. Kim, D. S. aut Enthalten in Russian journal of mathematical physics Pleiades Publishing, 1993 29(2022), 3 vom: Sept., Seite 358-377 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:29 year:2022 number:3 month:09 pages:358-377 https://doi.org/10.1134/S1061920822030050 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT AR 29 2022 3 09 358-377 |
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10.1134/S1061920822030050 doi (DE-627)OLC2131964269 (DE-He213)S1061920822030050-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kim, T. verfasserin aut Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. Kim, D. S. aut Enthalten in Russian journal of mathematical physics Pleiades Publishing, 1993 29(2022), 3 vom: Sept., Seite 358-377 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:29 year:2022 number:3 month:09 pages:358-377 https://doi.org/10.1134/S1061920822030050 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT AR 29 2022 3 09 358-377 |
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10.1134/S1061920822030050 doi (DE-627)OLC2131964269 (DE-He213)S1061920822030050-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kim, T. verfasserin aut Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. Kim, D. S. aut Enthalten in Russian journal of mathematical physics Pleiades Publishing, 1993 29(2022), 3 vom: Sept., Seite 358-377 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:29 year:2022 number:3 month:09 pages:358-377 https://doi.org/10.1134/S1061920822030050 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT AR 29 2022 3 09 358-377 |
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10.1134/S1061920822030050 doi (DE-627)OLC2131964269 (DE-He213)S1061920822030050-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kim, T. verfasserin aut Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. Kim, D. S. aut Enthalten in Russian journal of mathematical physics Pleiades Publishing, 1993 29(2022), 3 vom: Sept., Seite 358-377 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:29 year:2022 number:3 month:09 pages:358-377 https://doi.org/10.1134/S1061920822030050 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT AR 29 2022 3 09 358-377 |
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10.1134/S1061920822030050 doi (DE-627)OLC2131964269 (DE-He213)S1061920822030050-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kim, T. verfasserin aut Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2022 Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. Kim, D. S. aut Enthalten in Russian journal of mathematical physics Pleiades Publishing, 1993 29(2022), 3 vom: Sept., Seite 358-377 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:29 year:2022 number:3 month:09 pages:358-377 https://doi.org/10.1134/S1061920822030050 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT AR 29 2022 3 09 358-377 |
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Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices |
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Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. © Pleiades Publishing, Ltd. 2022 |
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Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. © Pleiades Publishing, Ltd. 2022 |
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Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds. © Pleiades Publishing, Ltd. 2022 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2131964269</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506063359.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230506s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S1061920822030050</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2131964269</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S1061920822030050-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">530</subfield><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kim, T.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</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">© Pleiades Publishing, Ltd. 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Dowling constructed the Dowling lattice $$Q_{n}(G)$$, for any finite set with $$n$$ elements and any finite multiplicative group $$G$$ of order $$m$$, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kind for any finite geometric lattice. These numbers for the Dowling lattice $$Q_{n}(G)$$ are the Whitney numbers of the first kind $$V_{m}(n,k)$$ and those of the second kind $$W_{m}(n,k)$$, which are given by Stirling number-like relations. In this paper, by ‘degenerating’ such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate $$r$$-Whitney numbers of both kinds.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kim, D. S.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Russian journal of mathematical physics</subfield><subfield code="d">Pleiades Publishing, 1993</subfield><subfield code="g">29(2022), 3 vom: Sept., Seite 358-377</subfield><subfield code="w">(DE-627)190282460</subfield><subfield code="w">(DE-600)1291704-7</subfield><subfield code="w">(DE-576)285631713</subfield><subfield code="x">1061-9208</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:29</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:3</subfield><subfield code="g">month:09</subfield><subfield code="g">pages:358-377</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1134/S1061920822030050</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">29</subfield><subfield code="j">2022</subfield><subfield code="e">3</subfield><subfield code="c">09</subfield><subfield code="h">358-377</subfield></datafield></record></collection>
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