Arithmetic Properties Satisfied by a Recent Integer Partition Function of Dombos

Mathematics > Number Theory [Submitted on 16 Jun 2026] Title:Arithmetic Properties Satisfied by a Recent Integer Partition Function of Dombos View PDF HTML (experimental)Abstract:In recent work of Dombos, the set of integer partitions of $n$ wherein the parts are either divisible by 4 or congruent to $\pm 1 \pmod{6}$ arose in a natural way. In this work, we will denote the function which counts the number of such partitions of $n$ by $dp(n)$. Using elementary generating function manipulations and classical $q$--series results, we prove several congruences satisfied by $dp(n)$. As an example, we prove that, for all $\alpha \geq 1$ and all $n \geq 0$, \begin{equation*} dp \left( 3^{2\alpha + 1}n + \frac{7 \cdot 9^\alpha + 1}{4} \right) \equiv 0 \pmod{3}. \end{equation*} Current browse context: math.NT References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.