ON PARTITION CONGRUENCES FOR OVERCUBIC PARTITION PAIRS
نویسندگان
چکیده
منابع مشابه
Arithmetic Properties of Overcubic Partition Pairs
Let b(n) denote the number of overcubic partition pairs of n. In this paper, we establish two Ramanujan type congruences and several infinite families of congruences modulo 3 satisfied by b(n). For modulus 5, we obtain one Ramanujan type congruence and two congruence relations for b(n), from which some strange congruences are derived.
متن کاملRamanujan type identities and congruences for partition pairs
Using elementary methods, we establish several new Ramanujan type identities and congruences for certain pairs of partition functions.
متن کاملElementary proofs of congruences for the cubic and overcubic partition functions
In 2010, Hei-Chi Chan introduced the cubic partition function a(n) in connection with Ramanujan’s cubic continued fraction. Chan proved that ∑ n≥0 a(3n+ 2)q = 3 ∏ i≥1 (1− q3n)3(1− q) (1− qn)4(1− q2n)4 which clearly implies that, for all n ≥ 0, a(3n+ 2) ≡ 0 (mod 3). In the same year, Byungchan Kim introduced the overcubic partition function a(n). Using modular forms, Kim proved that ∑ n≥0 a(3n +...
متن کاملPartition Statistics for Cubic Partition Pairs
In this brief note, we give two partition statistics which explain the following partition congruences: b(5n + 4) ≡ 0 (mod 5), b(7n + a) ≡ 0 (mod 7), if a = 2, 3, 4, or 6. Here, b(n) is the number of 4-color partitions of n with colors r, y, o, and b subject to the restriction that the colors o and b appear only in even parts.
متن کاملPartition congruences by involutions
We present a general construction of involutions on integer partitions which enable us to prove a number of modulo 2 partition congruences. Introduction The theory of partitions is a beautiful subject introduced by Euler over 250 years ago and is still under intense development [2]. Arguably, a turning point in its history was the invention of the “constructive partition theory” symbolized by F...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2012
ISSN: 1225-1763
DOI: 10.4134/ckms.2012.27.3.477