منابع مشابه
Computational Proofs of Congruences for 2-colored Frobenius Partitions
1. Background and introduction. In his 1984 Memoir of the American Mathematical Society, Andrews [2] introduced two families of partition functions, φk(m) and cφk(m), which he called generalized Frobenius partition functions. In this paper, we will focus our attention on one of these functions, namely cφ2(m), which denotes the number of generalized Frobenius partitions of m with 2 colors. In [2...
متن کاملA simple proof of some congruences for colored generalized frobenius partitions
where c#,Jr) is the number of F-partitions of r using h colors with (at most) s repetitions where s can be any positive integer or 00 (to represent no restriction on repetitions). The proofs of these congruences were based on some interesting congruence properties of compositions and were combinatorial in nature. Though the proofs were straightforward, they were somewhat lengthy and tedious. Du...
متن کاملCongruences for Generalized Frobenius Partitions with an Arbitrarily Large Number of Colors
In his 1984 AMS Memoir, George Andrews defined the family of k–colored generalized Frobenius partition functions. These are enumerated by cφk(n) where k ≥ 1 is the number of colors in question. In that Memoir, Andrews proved (among many other things) that, for all n ≥ 0, cφ2(5n+3) ≡ 0 (mod 5). Soon after, many authors proved congruence properties for various k–colored generalized Frobenius part...
متن کاملCongruences in ordered pairs of partitions
1. Introducing the birank. A partition is defined as being a nonincreasing sequence of positive integers, λ = (λ1,λ2, . . . ,λr ). The set of all partitions, which includes the empty partition ∅, is denoted by . The sum of the parts of a given partition is called the weight of the partition, wt(λ) = λ1+λ2+···+λr . It is standard notation to write (z;q)∞ := ∏ t≥0(1−zq) and p−k(n) for the coeffic...
متن کاملNew Congruences for Partitions where the Odd Parts are Distinct
Let pod(n) denote the number of partitions of n wherein odd parts are distinct (and even parts are unrestricted). We find some new interesting congruences for pod(n) modulo 3, 5 and 9.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1996
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0041