Institute of Mathematics

of the Czech Academy of Sciences
 
 
 
 

Czechoslovak Mathematical Journal, Vol. 71, No. 2, pp. 545-553, 2021

Combinatorial interpretations for identities using chromatic partitions

Mateus Alegri, Wagner Ferreira Santos, Samuel Brito Silva

Received December 21, 2019.   Published online February 2, 2021.
Abstract:  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.
Keywords:  integer partition; chromatic partition; Ferrers graph; partition identity
Classification MSC:  05A17, 11P82, 11P84
DOI:  10.21136/CMJ.2021.0542-19
PDF available at:  Springer   Institute of Mathematics CAS   Digital Mathematics Library
References:
[1] M. Alegri: On new identities involving chromatic overpartitions. J. Ramanujan Soc. Math. Math. Sci. 7 (2020), 109-118. Zbl 1448.05009
[2] G. E. Andrews: Partitions and Durfee dissection. Am. J. Math. 101 (1979), 735-742. DOI 10.2307/2373804 | MR 0533197 | Zbl 0409.10006
[3] G. E. Andrews, K. Eriksson: Integer Partitions. Cambridge University Press, Cambridge (2004). DOI 10.1017/CBO9781139167239 | MR 2122332 | Zbl 1073.11063
[4] D. M. Bressoud: A new family of partition identities. Pac. J. Math. 77 (1978), 71-74. DOI 10.2140/pjm.1978.77.71 | MR 0506017 | Zbl 0362.10016
[5] S. Corteel, J. Lovejoy: Overpartitions. Trans. Am. Math. Soc. 356 (2004), 1623-1635. DOI 10.1090/S0002-9947-03-03328-2 | MR 2034322 | Zbl 1040.11072
[6] L. Euler: De partitione numerorum, Caput XVI. Introductio in Analysin Infinitorum (A. Krazer, F. Rudio, eds.). Leonardi Euleri Opera Omnia, Series Prima, Volumen Octavum. B. G. Teubner, Leipzig (1922). (In Latin.) JFM 48.0007.02
[7] I. Pak: Partition bijections, a survey. Ramanujan J. 12 (2006), 5-75. DOI 10.1007/s11139-006-9576-1 | MR 2267263 | Zbl 1103.05009
Affiliations:   Mateus Alegri (corresponding author), Wagner Ferreira Santos, Samuel Brito Sila, University of Sergipe, Av. Vereador Olímpio Grande, s/n, Itabaiana, Sergipe, Brazil, e-mail: allegri.mateus@gmail.com, wagnermaths@gmail.com, s.complexo@hotmail.com
Springer subscribers can access the papers on Springer website.
[List of online first articles] [Contents of Czechoslovak Mathematical Journal] [Full text of the older issues of Czechoslovak Mathematical Journal at DML-CZ]
© Institute of Mathematics CAS, 2024



 
PDF available at:


Springer
for subscribers
···

Institute of Mathematics CAS
free access
···

Digital Mathematics Library
free access