Infinite Families of Congruences for Partition Functions EO(n) and EOe(n)
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In 2018, Andrews introduced the partition functions EO(n) and EO(n). The first of these denotes the number of partitions of n in which every even part is less than each odd part, and the second counts the number of partitions enumerated by the first in which only the largest even part appears an odd number of times. In 2021, Pore and Fathima introduced a new partition function E Oe(n) which counts the number of parti tions of n which are enumerated by E O(n) together with the partitions enumerated by E O(n) where all parts are odd and the number of parts is even. They also proved some particular congruences for E O(n) and E Oe(n). In this paper, we establish infinitely many families of congruences modulo 2, 4, 5 and 8 for E O(n) and modulo 4 for E Oe(n).
Abstract
In 2018, Andrews introduced the partition functions EO(n) and EO(n). The first of these denotes the number of partitions of n in which every even part is less than each odd part, and the second counts the number of partitions enumerated by the first in which only the largest even part appears an odd number of times. In 2021, Pore and Fathima introduced a new partition function E Oe(n) which counts the number of parti tions of n which are enumerated by E O(n) together with the partitions enumerated by E O(n) where all parts are odd and the number of parts is even. They also proved some particular congruences for E O(n) and E Oe(n). In this paper, we establish infinitely many families of congruences modulo 2, 4, 5 and 8 for E O(n) and modulo 4 for E Oe(n).
참고문헌 (9)
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