On a restricted m-ary partition function
نویسندگان
چکیده
منابع مشابه
On m–ary Partition Function Congruences: A Fresh Look at a Past Problem
Let bm(n) denote the number of partitions of n into powers of m. Define σr = ε2m 2 + ε3m 3 + · · · + εrm, where εi = 0 or 1 for each i. Moreover, let cr = 1 if m is odd, and cr = 2 r−1 if m is even. The main goal of this paper is to prove the congruence bm(m n− σr −m) ≡ 0 (mod m/cr). For σr = 0, the existence of such a congruence was conjectured by R. F. Churchhouse some thirty years ago, and i...
متن کاملOn Explicit Formula for Restricted Partition Function
A new recursive procedure of the calculation of a restricted partition function is suggested. An explicit combinatorial formula for the restricted partition function is found based on this procedure.
متن کاملOn Popoviciu Type Formulas for Generalized Restricted Partition Function
Suppose that a1(n), a2(n), · · · , as(n),m(n) are integer-valued polynomials in n with positive leading coefficients. This paper presents Popoviciu type formulas for the generalized restricted partition function pA(n)(m(n)) := #{(x1, · · · , xs) ∈ Z s : all x j > 0, x1a1(n) + · · · + xsas(n) = m(n)} when s = 2 or 3. In either case, the formula implies that the function is an integer-valued quas...
متن کاملCanonical (m,n)−ary hypermodules over Krasner (m,n)−ary hyperrings
The aim of this research work is to define and characterize a new class of n-ary multialgebra that may be called canonical (m, n)&minus hypermodules. These are a generalization of canonical n-ary hypergroups, that is a generalization of hypermodules in the sense of canonical and a subclasses of (m, n)&minusary hypermodules. In addition, three isomorphism theorems of module theory and canonical ...
متن کاملGeneralized Congruence Properties of the Restricted Partition Function P (n,m)
Ramanujan-type congruences for the unrestricted partition function p(n) are well known and have been studied in great detail. The existence of Ramanujan-type congruences are virtually unknown for p(n,m), the closely related restricted partition function that enumerates the number of partitions of n into exactly m parts. Let ` be any odd prime. In this paper we establish explicit Ramanujan-type ...
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: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2003.06.013