| Title:
|
Combinatorial interpretations for identities using chromatic partitions (English) |
| Author:
|
Alegri, Mateus |
| Author:
|
Ferreira Santos, Wagner |
| Author:
|
Brito Silva, Samuel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
545-553 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities. (English) |
| Keyword:
|
integer partition |
| Keyword:
|
chromatic partition |
| Keyword:
|
Ferrers graph |
| Keyword:
|
partition identity |
| MSC:
|
05A17 |
| MSC:
|
11P82 |
| MSC:
|
11P84 |
| idZBL:
|
07361084 |
| idMR:
|
MR4263185 |
| DOI:
|
10.21136/CMJ.2021.0542-19 |
| . |
| Date available:
|
2021-05-20T13:47:03Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148920 |
| . |
| Reference:
|
[1] Alegri, M.: On new identities involving chromatic overpartitions.J. Ramanujan Soc. Math. Math. Sci. 7 (2020), 109-118. Zbl 1448.05009 |
| Reference:
|
[2] Andrews, G. E.: Partitions and Durfee dissection.Am. J. Math. 101 (1979), 735-742. Zbl 0409.10006, MR 0533197, 10.2307/2373804 |
| Reference:
|
[3] Andrews, G. E., Eriksson, K.: Integer Partitions.Cambridge University Press, Cambridge (2004). Zbl 1073.11063, MR 2122332, 10.1017/CBO9781139167239 |
| Reference:
|
[4] Bressoud, D. M.: A new family of partition identities.Pac. J. Math. 77 (1978), 71-74. Zbl 0362.10016, MR 0506017, 10.2140/pjm.1978.77.71 |
| Reference:
|
[5] Corteel, S., Lovejoy, J.: Overpartitions.Trans. Am. Math. Soc. 356 (2004), 1623-1635. Zbl 1040.11072, MR 2034322, 10.1090/S0002-9947-03-03328-2 |
| Reference:
|
[6] Euler, L.: De partitione numerorum, Caput XVI.Introductio in Analysin Infinitorum Leonardi Euleri Opera Omnia, Series Prima, Volumen Octavum. B. G. Teubner, Leipzig (1922), A. Krazer, F. Rudio Latin \99999JFM99999 48.0007.02. MR 0016336 |
| Reference:
|
[7] Pak, I.: Partition bijections, a survey.Ramanujan J. 12 (2006), 5-75. Zbl 1103.05009, MR 2267263, 10.1007/s11139-006-9576-1 |
| . |
