Online Journal of Analytic Combinatorics

ISSN 1931-3365 (online)

The Online Journal of Analytic Combinatorics (OJAC) is a peer-reviewed electronic journal, originally hosted by the University of Rochester and now published by Combinatorial Press. The journal provides a high-quality platform for research at the intersection of analysis, number theory, and combinatorics, with particular emphasis on the convergence and interplay of these disciplines.
Open Access: OJAC follows the Diamond Open Access model—completely free for both authors and readers, with no APCs. 
Publication Frequency: The journal publishes articles on a continuous publication model, ensuring that accepted papers appear online promptly once finalized.
Scope: OJAC publishes research at the interface of analysis, number theory, and combinatorics, with a particular focus on the interplay and convergence of these fields. 
Indexing & Abstracting: Indexed in MathSciNet, zbMATH, and Scopus, ensuring strong visibility and scholarly recognition within the global mathematical community.
Rapid Publication: Accepted papers are published online immediately after final acceptance, providing timely access to new research findings.
Online Editions: OJAC is published exclusively in online format, reflecting its fully digital and open-access mission.

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Archive

A remark on Bourgain’s distributional inequality on the Fourier spectrum of Boolean functions

Hamed Hatami 1
1Department of Computer Science University of Toronto
Abstract:

Bourgain’s theorem says that under certain conditions a function \( f : \{0,1\}^n \to \{0,1\} \) can be approximated by a function \( g \) which depends only on a small number of variables. By following his proof we obtain a generalization for the case that there is a nonuniform product measure on the domain of \( f \).

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Fixed points of maps on the space of rational functions

Edward Mosteig1
1Department of Mathematics Loyola Marymount University Los Angeles, California 90045
Abstract:

Given integers \( s, t \), define a function \( \phi_{s,t} \) on the space of all formal series expansions by \(\phi_{s,t}\left(\sum a_n x^n\right) = \sum a_{sn+t} x^n.\) For each function \( \phi_{s,t} \), we determine the collection of all rational functions whose Taylor expansions at zero are fixed by \( \phi_{s,t} \). This collection can be described as a subspace of rational functions whose basis elements correspond to certain \( s \)-cyclotomic cosets associated with the pair \( (s, t) \).

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Sums of squares and triangular numbers

Hershel M. Farkas1
1Institute of Mathematics The Hebrew University Jerusalem
Abstract:

In this note we use the theory of theta functions to discover formulas for the number of representations of N as a sum of three squares and for the number of representations of N as a sum of three triangular numbers. We discover various new relations between these functions and short, motivated proofs of well known formulas of related combinatorial and number-theoretic interest.

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