ON ANDREWS’ PARTITION FUNCTION EO(n)

다국어 초록 (Multilingual Abstract)

Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper, we prove new congruences for EO(n) and pD(n), the number of partitions into distinct (or, odd) parts. We further establish linear recurrence relations for pD(n), which counts the number of partitions of n into distinct parts with 2 types of each part and EO(n).

참고문헌 (Reference)

1 J. Lovejoy, "The number of partitions into distinct parts modulo powers of 5" 35 : 41-46, 2003

2 J. Lovejoy, "The divisibility and distribution of partitons into distinct parts" 158 : 253-263, 2001

3 S. Ahlgren, "The arithemetic of partitions into distinct parts" 48 : 203-211, 2001

4 G. E. Andrews, "The Theory of Partitions" Cambridge Univ. Press 1998

5 M. D. Hirschhorn, "The Power of q" Springer 49 : 2017

6 B. C. Berndt, "Ramanujans Notebooks, Part III" Springer 1991

7 S. Corteel, "Overpartitions" 356 : 1623-1635, 2004

8 N. D Baruah, "On exact generating functions for the number of partitions into distinct parts" 14 : 1995-2011, 2018

9 R. Barman, "On Andrews' integer partitions with even parts below odd parts"

10 M. Merca, "New relations for the number of partitions with distinct even parts" 176 : 1-12, 2017

11 G. E. Andrews, "Integer partitions with even parts below odd parts and the mock theta func-tions" 22 : 433-445, 2018

12 M. D. Hirschhorn, "Elementary proofs of parity results for 5-regular partitions" 81 : 58-63, 2010

13 Φ. Rτdseth, "Congruence properties of the partition functions q(n)and q0(n)" 13 : 3-27, 1969

14 S. P Cui, "Arithmetic properties of l-regular partitions" 51 : 507-523, 2013

15 M. S. Mahadeva Naika, "Arithmetic properties of 5-regular partitions" 165 : 937-956, 2017