PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2015 | 63 | 2 | 123-140
Tytuł artykułu

Some Parity Statistics in Integer Partitions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study integer partitions with respect to the classical word statistics of levels and descents subject to prescribed parity conditions. For instance, a partition with summands $λ₁ ≥ ⋯ ≥ λ_k$ may be enumerated according to descents $λ_i > λ_{i+1}$ while tracking the individual parities of $λ_i$ and $λ_{i+1}$. There are two types of parity levels, E = E and O = O, and four types of parity-descents, E > E, E > O, O > E and O > O, where E and O represent arbitrary even and odd summands. We obtain functional equations and explicit generating functions for the number of partitions of n according to the joint occurrence of the two levels. Then we obtain corresponding results for the joint occurrence of the four types of parity-descents. We also provide enumeration results for the total number of occurrences of each statistic in all partitions of n together with asymptotic estimates for the average number of parity-levels in a random partition.
Słowa kluczowe
Twórcy
  • School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
  • Department of Mathematics, University of Haifa, 3498838 Haifa, Israel
  • School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-2-3
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.