The overpartition function modulo small powers of 2

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The overpartition function modulo small powers of 2

In a recent paper, Fortin, Jacob and Mathieu [5] found congruences modulo powers of 2 for the values of the overpartition function p(n) in arithmetic progressions. The moduli for these congruences ranged as high as 64. This note shows that p(n) ≡ 0 (mod 64) for a set of integers of arithmetic density 1.

متن کامل

The Overpartition Function modulo 128

Let p(n) denote the overpartition function. In a recent paper, K. Mahlburg showed that p(n) ≡ 0 (mod 64) for a set of integers of arithmetic density 1. In this paper, we will prove that p(n) ≡ 0 (mod 128) for almost all integers n.

متن کامل

Powers of Two Modulo Powers of Three

Since 2 is a primitive root of 3 for each positive integer m, the set of points {(n, 2 mod 3) : n > 0}, viewed as a subset of Z>0×Z>0 is bi-periodic, with minimal periods φ(3) (horizontally) and 3 (vertically). We show that if one considers the classes of n modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of...

متن کامل

Congruences modulo Prime Powers

Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α ⌊n/p i ⌋ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas' theorem: If α > 1 and l, s, t are nonnegative integers with s, t < p, then 1 ⌊n/p α−1 ⌋! k≡r (...

متن کامل

Congruences modulo high powers of 2 for Sloane's box stacking function

We are given n boxes, labeled 1, 2, . . . , n. Box i weighs i grams and can support a total weight of i grams. The number of different ways to build a single stack of boxes in which no box will be squashed by the weight of the boxes above it is denoted by f(n). In a 2006 paper, the first author asked for “congruences for f(n) modulo high powers of 2”. In this note, we accomplish this task by pr...

متن کامل

ذخیره 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.2004.03.014