Some Parity Statistics in Integer Partitions

• Autorzy: Blecher A. , Mansour T. , Munagi A. O.

Identyfikatory

DOI

10.4064/ba63-2-3

• 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

EN

partition; descent,; level; generating function; formula

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: Vol. 63, no. 2
• Strony: 123--140
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Blecher A.

• School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

autor

Mansour T.

• Department of Mathematics, University of Haifa, 3498838 Haifa, Israel

autor

Munagi A. O.

• School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa

Bibliografia

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