Add to ORKGAbstract. In a recent work, the authors provided the first-ever characteri-zation of the values bm(n) modulo m where bm(n) is the number of (unre-stricted) m-ary partitions of the integer n and m ≥ 2 is a fixed integer. That characterization proved to be quite elegant and relied only on the base m rep-resentation of n. Since then, the authors have been motivated to consider a specific restricted m-ary partition function, namely cm(n), the number of m-ary partitions of n where there are no “gaps ” in the parts. (That is to say, if mi is a part in a partition counted by cm(n), and i is a positive integer, then mi−1 must also be a part in the partition.) Using tools similar to those utilized in the aforementioned work on bm(n), we prove the fi...
Let n be a positive integer. A partition of n is a sequence of non-increasing positive integ...
The ordinary partition function p(n) counts the number of representations of a positive integer n as...
AbstractThe partition function P(n) satisfy some congruence properties. Eichhorn and Ono prove the e...
Abstract. Motivated by a recent conjecture of the second author related to the ternary partition fun...
For a fixed integer m ≥ 2, we say that a partition n = p1 + p2 + · · · + pk of a natural number n ...
AbstractLet bm(n) denote the number of partitions of n into powers of m. Define σr=ε2m2+ε3m3+…+εrmr,...
Let bm(n) denote the number of partitions of n into powers of m. Define σr = ε2m 2 + ε3m 3 + · · ·...
AbstractWe discuss a family of restricted m-ary partition functions bm,j(s)(n), which is the number ...
AbstractAn M-partition of a positive integer m is a partition of m with as few parts as possible suc...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
M.V. Subbarao proved that the number of partitions of $n$ in which parts occur with multiplicities 2...
AbstractLet p(n) be the number of partitions of a non-negative integer n. In this paper we prove tha...
The first chapter examines $p_b(n)$, the number of partitions of $n$ into powers of $b$, along with ...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
Let n be a positive integer. A partition of n is a sequence of non-increasing positive integ...
The ordinary partition function p(n) counts the number of representations of a positive integer n as...
AbstractThe partition function P(n) satisfy some congruence properties. Eichhorn and Ono prove the e...
Abstract. Motivated by a recent conjecture of the second author related to the ternary partition fun...
For a fixed integer m ≥ 2, we say that a partition n = p1 + p2 + · · · + pk of a natural number n ...
AbstractLet bm(n) denote the number of partitions of n into powers of m. Define σr=ε2m2+ε3m3+…+εrmr,...
Let bm(n) denote the number of partitions of n into powers of m. Define σr = ε2m 2 + ε3m 3 + · · ·...
AbstractWe discuss a family of restricted m-ary partition functions bm,j(s)(n), which is the number ...
AbstractAn M-partition of a positive integer m is a partition of m with as few parts as possible suc...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
M.V. Subbarao proved that the number of partitions of $n$ in which parts occur with multiplicities 2...
AbstractLet p(n) be the number of partitions of a non-negative integer n. In this paper we prove tha...
The first chapter examines $p_b(n)$, the number of partitions of $n$ into powers of $b$, along with ...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
Let n be a positive integer. A partition of n is a sequence of non-increasing positive integ...
The ordinary partition function p(n) counts the number of representations of a positive integer n as...
AbstractThe partition function P(n) satisfy some congruence properties. Eichhorn and Ono prove the e...