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
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