The National Humanities Center (NHC) is an independent institute located in the United States that is dedicated to advancing research in the humanities. Founded in 1978, it is one of the leading organizations in promoting scholarship in areas such as history, literature, philosophy, and cultural studies. The Center provides support for researchers through fellowships, resources, and various programs aimed at fostering interdisciplinary research and collaboration among scholars in the humanities.

Robert Kirby-Harris is not widely recognized in mainstream media or prominent historical contexts, so there may be limited public information about him. If you are looking for a specific individual, it may help to provide additional context, such as their profession or relevance to a certain field. It’s also possible that he may be a private individual or a figure in a specialized area.

Harry Leinweber may refer to an individual's name, but without additional context, it's difficult to provide specific information. It’s possible he could be a public figure, a scholar, or someone known in a particular field.

Martin Copley is a name that might refer to various individuals; however, one notable Martin Copley is a British conservationist and wildlife filmmaker known for his work in promoting and documenting wildlife and environmental issues. He has made contributions to wildlife conservation and has been involved with several projects focused on preserving natural habitats and species.

A binary sequence is a sequence of numbers where each number is either a 0 or a 1. These sequences are fundamental in various fields, particularly in computer science and digital electronics, as they represent the most basic form of data storage and processing. ### Characteristics of Binary Sequences: 1. **Composition**: Each element of the sequence can take on one of two possible values: 0 or 1.

The concept of alternating factorial refers to a specific way of calculating a factorial that alternates the signs of the terms. For a non-negative integer \( n \), the alternating factorial \( !n \) is defined as follows: \[ !

An arithmetic number is not a standard term widely recognized in mathematics, but it could refer to different concepts depending on the context. Here are a couple of interpretations: 1. **Arithmetic Sequences**: In the context of sequences, an arithmetic number could refer to the numbers in an arithmetic sequence, which is a sequence of numbers in which the difference between any two consecutive terms is constant. For example, in the sequence 2, 5, 8, 11, ...

An **automatic sequence** is a type of numerical sequence that is generated by a specific rule or algorithm, often involving a function or a set of operations that can be repeated indefinitely. The defining characteristic of an automatic sequence is that it can be described by a finite automaton, which means that given any input (usually an integer representing the position in the sequence), the automaton can produce the corresponding term in the sequence without the need for memory of past values.

Delannoy numbers are a type of combinatorial number that counts the number of different paths from the bottom-left corner to the top-right corner of an \( m \times n \) grid, where you can move only to the right, up, or diagonally up-right at each step. The Delannoy number \( D(m, n) \) represents the total number of such paths.

A Double Mersenne number is a special class of numbers that is defined using Mersenne numbers. Mersenne numbers are of the form \( M_n = 2^n - 1 \), where \( n \) is a positive integer. A Double Mersenne number is then defined as a Mersenne number whose index \( n \) itself is a Mersenne prime.

The Erdős–Nicolas number is a concept from combinatorial number theory that is associated with a particular type of partitioning of the natural numbers. Specifically, it's named after the mathematicians Paul Erdős and Michel Nicolas, who studied certain properties of numbers and sequences.

A fractal sequence is a series of elements that exhibit a recursive or self-similar structure, often characterized by repeating patterns at various scales. In mathematics and specifically in the field of fractal geometry, a fractal is often defined through its property of self-similarity, meaning that parts of the fractal resemble the whole structure.

A highly abundant number is a positive integer that has a particularly high ratio of the sum of its divisors to the number itself. More formally, a highly abundant number \( n \) satisfies the condition that for any integer \( m < n \), the sum of the divisors function \( \sigma(m) \) (which returns the sum of all positive divisors of \( m \)) is less than \( \sigma(n) \) divided by \( n \).

Hooley's delta function, often denoted as \( \Delta(s) \), is a mathematical tool used in number theory, particularly in the context of the Generalized Riemann Hypothesis and the distribution of prime numbers. It was introduced by C. Hooley in his work related to the study of integers represented by quadratic forms and sieve methods. The function is defined in terms of the values of L-functions, specifically for certain Dirichlet series associated with characters.

The Journal of Integer Sequences (JIS) is a peer-reviewed open-access journal that publishes research articles focused on the study of integer sequences. It is dedicated to the examination and exploration of sequences of integers, which are critical in various fields such as mathematics, computer science, and number theory. The journal was established in 1998, and it operates under the auspices of the University of Missouri.

A Lobb number is a term used in the context of graph theory to refer to a specific characteristic of a graph related to its properties concerning the number of edges and vertices. However, the term "Lobb number" might not be widely recognized or defined in standardized graph theory literature.

Lucas numbers are a sequence of numbers that are similar to the Fibonacci numbers but start with different initial values. The Lucas sequence is defined as follows: 1. The first two terms of the sequence are \(L_0 = 2\) and \(L_1 = 1\).

A Mersenne prime is a specific type of prime number that can be expressed in the form \(M_n = 2^n - 1\), where \(n\) is a positive integer. In other words, if \(M_n\) is prime, then \(n\) itself must also be prime.

The Motzkin numbers are a sequence of natural numbers that arise in various combinatorial contexts. The \(n\)th Motzkin number, denoted as \(M_n\), counts the number of ways to draw non-intersecting chords connecting \(n\) points on a circle to the diameter below, without any chords crossing each other. Additionally, it can represent the number of monotonic paths along the edges of a grid.

In number theory and combinatorics, the **partition function** is a function that counts the number of distinct ways a given positive integer can be expressed as a sum of positive integers, regardless of the order of addends.