Guidelines for Mathematical Notation

General Principles

Mathematical notation should prioritize clarity, consistency, and readability.

Authors are encouraged to:

• use notation consistently throughout the manuscript;
• define variables, parameters, and symbols when first introduced;
• follow standard conventions whenever possible; and
• avoid unnecessarily complex or ambiguous notation.

Notation should support the communication of ideas rather than maximize compactness or symbolic density.

Mathematical notation should remain consistent across the main text, appendices, tables, figures, algorithms, and supplementary materials.

LaTeX Templates & Style Files

For manuscripts containing substantial mathematical content, authors are encouraged to prepare submissions in LaTeX whenever practical.

INFORMS manuscript templates and class files are available to support consistent manuscript preparation and formatting.

Variables & Symbols

Variables are generally set in italic type, while mathematical operators, function names, abbreviations, and descriptive subscripts are typically set in upright (roman) type.

Vectors are typically presented in boldface type to distinguish them from scalar variables.

Authors should:

• distinguish clearly between variables, constants, vectors, matrices, operators, and labels;
• avoid introducing multiple symbols with highly similar appearance; and
• use notation that remains legible when reduced to publication size.

Single-letter variables are often preferable for readability, particularly in dense mathematical expressions. However, descriptive multi-character notation may be appropriate when it improves clarity or reflects standard usage within a field.

When multi-word notation is necessary, authors are encouraged to use consistent conventions that clearly distinguish variables from ordinary text.

Greek Letters & Specialized Symbols

Greek letters and specialized mathematical symbols should be selected carefully to avoid ambiguity or visual confusion.

Authors should pay particular attention to:

• similar-looking symbols,
• superscripts and subscripts,
• boldface notation, and
• notation that may become difficult to distinguish at small sizes.

Care should be taken to distinguish visually similar characters and symbols, such as lowercase “l” and the numeral “1,” uppercase “O” and the numeral “0,” or Greek and Latin characters with similar appearance.

Equations & Mathematical Expressions

Equations should be presented in a manner that supports readability and logical flow.

Displayed Equations

Long or complex expressions should generally be displayed separately from the surrounding paragraph text rather than embedded inline.

Displayed equations should:

• use consistent alignment and spacing,
• be broken across lines where appropriate, and
• remain readable within the journal’s page and column layout.

Displayed equations that form part of a sentence should be punctuated consistently with the surrounding grammatical structure.

Authors are encouraged to simplify lengthy expressions when appropriate by introducing auxiliary notation or intermediate definitions.

Inline Mathematical Expressions

Inline mathematical expressions should be kept concise whenever possible.

Complex fractions, exponents, or nested expressions that interrupt reading flow may be clearer when reformulated or displayed separately.

Authors should avoid beginning sentences with mathematical notation or symbols whenever possible. Rewriting the sentence structure often improves readability and accessibility.

Equation Numbering

Authors are encouraged to number only equations that are referenced or discussed elsewhere in the manuscript. Equation numbering should be applied consistently throughout the manuscript.

Mathematical Operators & Functions

Standard mathematical operators and function names (for example, log, ln, exp, sin, max, min, Pr, and Cov) should be clearly distinguished from variables.

Authors should ensure that custom operators, abbreviations, optimization problem labels, and other specialized notation are introduced consistently and defined when first used.

Algorithms & Pseudocode

Algorithms and pseudocode should be formatted consistently and presented in a readable structure with clear indentation, notation, and labeling conventions.

Authors are encouraged to use notation and formatting that remain understandable in both print and digital publication formats.

Readability & Accessibility

INFORMS encourages authors to prepare mathematical content in ways that improve readability and accessibility for all readers, including readers using assistive technologies.

To improve accessibility, authors should:

• create equations using editable equation tools or LaTeX rather than images whenever possible;
• verify that equations, symbols, and special characters display correctly in both editable source files and submitted PDF versions;
• define variables, parameters, and symbols clearly when first introduced;
• avoid unnecessarily complex or deeply nested notation where possible;
• distinguish clearly between similar-looking symbols; and
• supplement mathematical expressions with explanatory prose when appropriate.

Dense notation should be introduced progressively to support readability in both visual and assistive reading environments.

Additional accessibility guidance is available in Preparing Manuscript & Figure Files.

Abstracts & Metadata

Because abstracts are widely distributed through indexing and metadata systems, authors should avoid mathematical notation in abstracts whenever possible.

If formulas or symbols are necessary, their use should be kept concise and limited to essential content.

Attribution & Prior Work

The reuse of commonly accepted notation, terminology, algorithms, and standard methodological frameworks is generally appropriate within scholarly communication, and reuse of notation for consistency is encouraged.

However, authors should appropriately acknowledge prior sources when mathematical models, analytical methods, proofs, algorithms, or conceptual frameworks originate from prior work and are not widely regarded as common knowledge within the field.

Changing notation or terminology does not eliminate the obligation to provide attribution where substantive intellectual contributions originate elsewhere.

Authors should clearly indicate whether a model, algorithm, proof, or other analytical contribution originates from prior literature or represents an original contribution of the submitted work.

Additional guidance is available in Originality, Attribution & Copyright.

Journal-Specific Considerations

Certain journals or article types may have additional expectations regarding mathematical presentation, notation, appendices, or equation formatting.

For example, some journals may:

• encourage concise mathematical presentation in the main text,
• prefer extensive derivations to appear in appendices or supplementary materials, or
• publish articles in layouts that accommodate longer displayed equations.

Authors should consult the journal-specific submission guidelines for additional requirements.