This problem became known as Kirkman's schoolgirl problem, subsequently to become Kirkman's most famous result.He published several additional works on combinatorial design theory in later years.…

There are many ways of thinking about the class of all combinatorial species.Since a species is a functor, it makes sense to say that the category of species is a functor category whose objects are species and whose arrows are natural transformations.…

These aspects form the input and output data space of the test object.The second step of test design then follows the principles of combinatorial test design.While the method can be applied using a pen and a paper, the usual way involves the usage of the Classification Tree Editor, a software tool implementing the classification tree method.…

One player, Left, plays tiles vertically, while the other, Right, plays horizontally.As in most games in combinatorial game theory, the first player who cannot move loses.Other than the empty game, where there is no grid, the simplest game is a single box.…

At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in Sudoku grids.Combinatorial design theory can be applied to the area of design of experiments.Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments.…

There are different rule-sets (Japanese, Chinese, AGA, etc.), which are almost entirely equivalent, except for certain special-case positions.In formal game theory terms, Go is a non-chance, combinatorial game with perfect information.…

The travelling salesman problem may be seen as a special case of QAP if one assumes that the flows connect all facilities only along a single ring, all flows have the same non-zero (constant) value.Many other problems of standard combinatorial optimization problems may be written in this form.In addition to the original plant location formulation, QAP is a mathematical model for the problem of placement of interconnected electronic components onto a printed circuit board or on a microchip, which is part of the place and route stage of computer aided design in the electronics industry.…

No sequential pattern generation is required - combinatorial tests, which are much easier to generate, will suffice.If you have a combinatorial test, it can be easily applied.In a chip that does not have a full scan design -- i.e., the chip has sequential circuits, such as memory elements that are not part of the scan chain, sequential pattern generation is required.…

The fact that systematicity and productivity depend on the compositional structure of language means that language has a combinatorial semantics.If thought also has such a combinatorial semantics, then there must be a language of thought.The second argument that Fodor provides in favour of representational realism involves the processes of thought.…

SOS is a game of skill and an abstract strategy game.It is also a combinatorial game (when played with two players).In terms of game theory, it is a zero-sum, sequential game with perfect information.…

Difficulties greatly increase in constructing systems with more numbers and combinations.In mathematics, the study of these objects falls within the branch of combinatorial design.Players are usually interested to have a certain guarantee in the minimum possible (or minimum known) number of tickets.…

The first two properties define a combinatorial structure known as an independence system.A subset of the ground set E that is not independent is called dependent.…

In combinatorial game theory, the zero game is the game where neither player has any legal options.Therefore, under the normal play convention, the first player automatically loses, and it is a second-player win.…

In 1902 Bouton published a solution of the game Nim.This result is today viewed as the birth of combinatorial game theory.…

The classical core of the subject of combinatorial designs is built around balanced incomplete block designs (BIBDs), Hadamard matrices and Hadamard designs, symmetric BIBDs, Latin squares, resolvable BIBDs, difference sets, and pairwise balanced designs (PBDs).Other combinatorial designs are related to or have been developed from the study of these fundamental ones.…

Every orbifold has associated with it an additional combinatorial structure given by a complex of groups.

The great difficulty (e.g. when computing the partition function of the system) is the treatment of combinatorics generated by the interaction terms in the Hamiltonian when summing over all states.The goal of mean field theory is to resolve these combinatorial problems.MFT is known under a great many names and guises.…

In combinatorial game theory, there are four types of game.

In number theory, zero-sum problems are a certain class of combinatorial questions.In general, a finite abelian group G is considered.…

On Numbers and Games was also a fruit of the collaboration between Berlekamp, Conway, and Guy.Combinatorial games are generally, by convention, put into a form where one player wins when the other has no moves remaining.It is easy to convert any finite game with only two possible results into an equivalent one where this convention applies.…