We investigate arithmetic and combinatorial properties of the function a(n), which is the signed number of partitions of n into exactly two distinct part sizes, each occurring an odd number of times. We prove that a(n)≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a(n)\ge 0$$\end{document} for all n, establishing a positivity phenomenon for a signed partition function arising from a double Lambert series. Furthermore, we show that a(n) satisfies nontrivial divisibility properties modulo 3. The results reveal unexpected arithmetic regularity in a family of partition functions defined by odd multiplicity constraints and restricted support.
This paper unifies disparate areas of combinatorics. Namely, graph theory and integer partition theory. A partition of an integer n is a finite sequence a1,a2,…,aj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
A. Blecher, A. Knopfmacher· The Ramanujan journal· 0 citations
Residue number systems based on pairwise relatively prime moduli are a powerful tool for accelerating integer computations via the Chinese Remainder Theorem. We study a structured family of moduli of the form 2n−2k+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...
Robert Dougherty-Bliss, Natalya Ter-Saakov, Mits Kobayashi et al.· Mathematics and Computer Sci...· 0 citations
In 1984, Bressoud and Subbarao established an interesting weighted partition identity connecting the partition function and the divisor function. Recently, the first author, jointly with Bhoria, Eyyunni, and Maji, extended the work of Bressoud and Subbarao and obtained the following analogous weighted partition identit...
We study the arithmetic of the K3 category associated to a cubic fourfold over a non-algebraically closed field k, specifically, the Galois representation on its ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
Asher Auel, Jack Petok· Research in Number Theory· 0 citations
This paper presents a comprehensive study of $n^r$-partitions, defined by the generating function $\prod_{n=1}^{\infty} (1 - q^n)^{-n^r}$, which interpolates analytically between ordinary partitions ($r=0$), plane partitions ($r=1$), and higher-dimensional combinatorial structures ($r\geq2$).
Our main contributions in...
M. Alegri, A. Christopher, E. V. Pereira Spreafico· Notes on Number Theory and D...· 0 citations
