Combinatorial interpretations for identities using chromatic partitions

Mateus Alegri; Wagner Ferreira Santos; Samuel Brito Silva

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 545-553
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Alegri, Mateus, Ferreira Santos, Wagner, and Brito Silva, Samuel. "Combinatorial interpretations for identities using chromatic partitions." Czechoslovak Mathematical Journal 71.2 (2021): 545-553. <http://eudml.org/doc/297880>.

@article{Alegri2021,
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.},
author = {Alegri, Mateus, Ferreira Santos, Wagner, Brito Silva, Samuel},
journal = {Czechoslovak Mathematical Journal},
keywords = {integer partition; chromatic partition; Ferrers graph; partition identity},
language = {eng},
number = {2},
pages = {545-553},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Combinatorial interpretations for identities using chromatic partitions},
url = {http://eudml.org/doc/297880},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Alegri, Mateus
AU - Ferreira Santos, Wagner
AU - Brito Silva, Samuel
TI - Combinatorial interpretations for identities using chromatic partitions
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 545
EP - 553
AB - 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.
LA - eng
KW - integer partition; chromatic partition; Ferrers graph; partition identity
UR - http://eudml.org/doc/297880
ER -

References

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  1. Alegri, M., On new identities involving chromatic overpartitions, J. Ramanujan Soc. Math. Math. Sci. 7 (2020), 109-118. (2020) Zbl1448.05009
  2. Andrews, G. E., 10.2307/2373804, Am. J. Math. 101 (1979), 735-742. (1979) Zbl0409.10006MR0533197DOI10.2307/2373804
  3. Andrews, G. E., Eriksson, K., 10.1017/CBO9781139167239, Cambridge University Press, Cambridge (2004). (2004) Zbl1073.11063MR2122332DOI10.1017/CBO9781139167239
  4. Bressoud, D. M., 10.2140/pjm.1978.77.71, Pac. J. Math. 77 (1978), 71-74. (1978) Zbl0362.10016MR0506017DOI10.2140/pjm.1978.77.71
  5. Corteel, S., Lovejoy, J., 10.1090/S0002-9947-03-03328-2, Trans. Am. Math. Soc. 356 (2004), 1623-1635. (2004) Zbl1040.11072MR2034322DOI10.1090/S0002-9947-03-03328-2
  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 9999JFM99999 48.0007.02. (1922) MR0016336
  7. Pak, I., 10.1007/s11139-006-9576-1, Ramanujan J. 12 (2006), 5-75. (2006) Zbl1103.05009MR2267263DOI10.1007/s11139-006-9576-1

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