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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2210.02566 |
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| _version_ | 1866909774986084352 |
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| author | Bang, Caroline von Bell, Matias Culver, Eric Dickson, Jessica Dimitrov, Stoyan Perrier, Rachel Sundaram, Sheila |
| author_facet | Bang, Caroline von Bell, Matias Culver, Eric Dickson, Jessica Dimitrov, Stoyan Perrier, Rachel Sundaram, Sheila |
| contents | We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the $A$- and $Z$-sequences of these sums of Riordan arrays, and also identify an analog for $A$-sequences when the sum of Riordan arrays does not yield a Riordan array. In addition, we define the new operations `Der' and `Flip' on Riordan arrays. We fully characterize the Riordan arrays resulting from these operations applied to the Appell and Lagrange subgroups of the Riordan group. Finally, we study the application of these operations to various known Riordan arrays, generating many combinatorial identities in the process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02566 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Sums, Derivatives, and Flips of Riordan Arrays Bang, Caroline von Bell, Matias Culver, Eric Dickson, Jessica Dimitrov, Stoyan Perrier, Rachel Sundaram, Sheila Combinatorics Rings and Algebras We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the $A$- and $Z$-sequences of these sums of Riordan arrays, and also identify an analog for $A$-sequences when the sum of Riordan arrays does not yield a Riordan array. In addition, we define the new operations `Der' and `Flip' on Riordan arrays. We fully characterize the Riordan arrays resulting from these operations applied to the Appell and Lagrange subgroups of the Riordan group. Finally, we study the application of these operations to various known Riordan arrays, generating many combinatorial identities in the process. |
| title | On Sums, Derivatives, and Flips of Riordan Arrays |
| topic | Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2210.02566 |