Ars Mathematica Contemporanea is a scientific journal that publishes research articles in the field of mathematics. It aims to provide a platform for the dissemination of high-quality research across various areas of mathematics, including but not limited to pure mathematics, applied mathematics, and mathematical applications in other scientific fields. The journal emphasizes contemporary issues and advancements in mathematical research, and it typically features peer-reviewed articles to ensure the integrity and quality of the published work.

The Australasian Journal of Combinatorics is a peer-reviewed academic journal that focuses on research in combinatorics, which is a branch of mathematics dealing with the counting, arrangement, and combination of objects. Established in 1990, the journal publishes original research papers, survey articles, and other contributions related to various aspects of combinatorial theory and applications.

Combinatorica is a software package for the Wolfram Language, which provides a wide range of tools for combinatorial and graph theory applications. It offers functions for working with permutations, combinations, and various combinatorial structures, including graphs, trees, and partitions. Users can utilize Combinatorica to perform explorations in combinatorial mathematics, generate random combinatorial objects, and visualize graph structures.

Coalescence in physics refers to the process by which two or more entities combine to form a single, larger entity. This phenomenon can be observed in various contexts, including: 1. **Fluid Dynamics**: In the context of fluid mechanics, coalescence often describes the merging of droplets or bubbles. For instance, smaller droplets of a liquid can merge to form larger droplets when they come into contact.

"The Chips Are Down" is a phrase that generally means a situation has reached a critical point where the outcome is uncertain and challenging decisions must be made. It is often used in contexts such as gambling, sports, or any competitive scenario where stakes are high and the pressure is on.

Discrete Mathematics and Theoretical Computer Science are two interrelated fields that contribute significantly to computer science as a whole. Here's a brief overview of each: ### Discrete Mathematics Discrete Mathematics is a branch of mathematics that deals with discrete (as opposed to continuous) objects. It includes a variety of topics that are foundational to computer science, including: 1. **Set Theory**: The study of sets, which are collections of objects.

"Discrete Mathematics" is a scholarly journal that publishes original research articles on various aspects of discrete mathematics. This area of mathematics encompasses a wide range of topics, including graph theory, combinatorics, algorithms, discrete probability, and number theory, among others. The journal serves as a platform for researchers to share their findings, discuss theories, and explore applications in computer science, information theory, and related fields.

Graphs and combinatorics are interconnected fields of mathematics that study structures and arrangements, often with applications in computer science, optimization, and other areas. ### Graphs A **graph** is a collection of nodes (or vertices) connected by edges. Graph theory is the study of these graphs and their properties.

The Journal of Combinatorial Theory is a mathematical journal that focuses on combinatorial mathematics, which is the study of discrete structures and their properties. It typically covers a wide range of topics within combinatorics, including graph theory, design theory, extremal combinatorics, enumerative combinatorics, and combinatorial optimization, among others. The journal publishes original research articles, surveys, and occasionally special issues, featuring contributions that advance the field and provide new insights into combinatorial concepts and methods.

Equation "Hydrogen spectral series mnemonic" gives for example from principal quantum number 1 to 2 a difference:which with Planck-Einstein relation gives about 121.6 nm ($2.47\times 10^{1}5$ Hz), which is a reasonable match with the value of 121.567... from the NIST Atomic Spectra Database.

The **Journal of Graph Theory** is a peer-reviewed academic journal that focuses on the field of graph theory, a branch of mathematics and computer science that studies the properties and applications of graphs, which are mathematical structures used to model pairwise relations between objects. The journal publishes original research articles, review papers, and occasionally special issues covering various aspects of graph theory, including its applications in areas such as computer science, biology, social networks, and operations research.

Algorithmic combinatorics on partial words is a specialized area of combinatorics that deals with the study of combinatorial structures that arise from partial words. A partial word can be thought of as a sequence of symbols that may include some "undefined" or "unknown" positions, often represented by a special symbol (like a question mark or a dot). ### Key Concepts: 1. **Partial Words**: These are sequences where some characters are unspecified.

A Davenport–Schinzel sequence is a specific type of sequence formed by applying certain restrictions on the allowable subsequences. Named after mathematicians H. Davenport and A. Schinzel, these sequences arise in the context of combinatorial geometry and computational geometry. In a Davenport–Schinzel sequence, the sequences consist of elements drawn from a finite set, typically called the alphabet set, subject to specific constraints.

A "free lattice" typically refers to a type of lattice in the context of lattice theory, a branch of mathematics that studies ordered sets and their properties. In lattice theory, a lattice is a partially ordered set in which any two elements have a unique supremum (least upper bound, also known as join) and an infimum (greatest lower bound, or meet).

A **Lyndon word** is a non-empty string that is strictly smaller than all of its nontrivial suffixes in the lexicographical order. More formally, a string \( w \) is called a Lyndon word if it cannot be written as a nontrivial concatenation of two smaller strings, i.e.

A "partial word" generally refers to a segment or piece of a word that is not complete. It can involve a few letters of a word that may not fully convey its meaning or pronunciation. Partial words are often used in contexts such as: 1. **Word Formation**: When creating new words or forms, prefixes or suffixes might be considered partial words.