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- Combinatorial design

Lam's problem

In finite geometry, Lam's problem is the problem of determining if a finite projective plane of order ten exists.The order ten case is the first theoretically uncertain case, as all smaller orders can

Combinatorial design

Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concept

Regular tuning

Among alternative guitar-tunings, regular tunings have equal musical intervals between the paired notes of their successive open strings. Guitar tunings assign pitches to the open strings of guitars.

Steiner system

In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2. A Steiner system with parameters

Hadamard's maximal determinant problem

Hadamard's maximal determinant problem, named after Jacques Hadamard, asks for the largest determinant of a matrix with elements equal to 1 or −1. The analogous question for matrices with elements equ

Williamson conjecture

In combinatorial mathematics, specifically in combinatorial design theory and combinatorial matrix theory the Williamson conjecture is that Williamson matrices of order exist for all positive integers

Kirkman's schoolgirl problem

Kirkman's schoolgirl problem is a problem in combinatorics proposed by Rev. Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states: Fifteen young

Room square

A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that: 1.
* Each cell of the array is either empty or contains an unordered pair from

Social golfer problem

In discrete mathematics, the social golfer problem (SGP) is a combinatorial-design problem derived from a question posted in the usenet newsgroup sci.op-research in May 1998. The problem is as follows

Weighing matrix

In mathematics, a weighing matrix of order and weight is a matrix with entries from the set such that: Where is the transpose of and is the identity matrix of order . The weight is also called the deg

Block design

In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that frequency of the elements satisfies certa

Hadamard matrix

In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometric term

Ruzsa–Szemerédi problem

In combinatorial mathematics and extremal graph theory, the Ruzsa–Szemerédi problem or (6,3)-problem asks for the maximum number of edges in a graph in which every edge belongs to a unique triangle.Eq

Turán number

In mathematics, the Turán number T(n,k,r) for r-uniform hypergraphs of order n is the smallest number of r-edges such that every induced subgraph on k vertices contains an edge. This number was determ

Unital (geometry)

In geometry, a unital is a set of n3 + 1 points arranged into subsets of size n + 1 so that every pair of distinct points of the set are contained in exactly one subset. n ≥ 3 is required by some auth

Balanced tournament design

No description available.

Fisher's inequality

Fisher's inequality is a necessary condition for the existence of a balanced incomplete block design, that is, a system of subsets that satisfy certain prescribed conditions in combinatorial mathemati

Orthogonal array

In mathematics, an orthogonal array is a "table" (array) whose entries come from a fixed finite set of symbols (typically, {1,2,...,n}), arranged in such a way that there is an integer t so that for e

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