Glossary of chess

This page explains commonly used terms in chess in alphabetical order. Some of these have their own pages, like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of chess-related games, see Chess variants.

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[adjective: prophylactic] Prophylactic techniques include the blockade, overprotection, and the mysterious rook move.

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References

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Chess

Chess is a two-player board game played on a chessboard, a checkered gameboard with 64 squares arranged in an eight-by-eight grid. Chess is played by millions of people worldwide, both amateurs and professionals.

Each player begins the game with 16 pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns. Each of the six piece types moves differently. The most powerful piece is the queen and the least powerful piece is the pawn. The objective is to 'checkmate' the opponent's king by placing it under an inescapable threat of capture. To this end, a player's pieces are used to attack and capture the opponent's pieces, while supporting their own. In addition to checkmate, the game can be won by voluntary resignation by the opponent, which typically occurs when too much material is lost, or if checkmate appears unavoidable. A game may also result in a draw in several ways.

Chess is believed to have originated in India, some time before the 7th century; the Indian game of chaturanga is also the likely ancestor of xiangqi and shogi. The pieces took on their current powers in Spain in the late 15th century; the rules were finally standardized in the 19th century.

Chess annotation symbols

When annotating chess games, commentators frequently use widely recognized annotation symbols. Question marks and exclamation points that denote a move as bad or good are ubiquitous in chess literature. Some publications intended for an international audience, such as the Chess Informant have a wide range of additional symbols that transcend language barriers.

The common symbols for evaluating the merits of a move are "??", "?", "?!", "!?", "!", and "!!". In these cases, the corresponding symbol is juxtaposed in the text immediately after the move (e.g. Re7? or Kh1!?, see algebraic chess notation).

Use of these annotation symbols is subjective, as different annotators use the same symbols differently. Moreover, an annotator's use of symbols is often influenced by the player's strength: a positional misjudgment that an annotator might give a "??" if played by a strong grandmaster might pass unremarked if played by a beginner.

Annotators' use of punctuation also may possibly be influenced by the result of the game (regardless of the actual quality of the move); one possible example came in the 11th game of the 1972 World Championship, when Spassky played an unexpected move, 14.Nb1, retreating the knight to its initial square. Spassky won the game, and several annotators gave the move two exclamation points. Edmar Mednis asserted that if Spassky had lost the game, the move would likely have been given two question marks instead.

Computer chess

Computer chess is computer architecture encompassing hardware and software capable of playing chess autonomously without human guidance. Computer chess acts as solo entertainment (allowing players to practice and to better themselves when no sufficiently strong human opponents are available), as aids to chess analysis, for computer chess competitions, and as research to provide insights into human cognition.

Current chess engines are able to defeat even the strongest human players under normal conditions. Whether computation could ever solve chess remains an open question.

Availability

Chess-playing computers are now accessible to the average consumer. From the mid-1970s to the present day, dedicated chess computers have been available for purchase. There are many chess engines such as Stockfish, Crafty, Fruit and GNU Chess that can be downloaded from the Internet for free. These engines are able to play a game that, when run on an up-to-date personal computer, can defeat most master players under tournament conditions. Top programs such as the proprietary Shredder or Fritz or the open source program Stockfish have surpassed even world champion caliber players at blitz and short time controls. In October 2008 Rybka was rated top in the CCRL,CEGT, CSS,SSDF, and WBEC rating lists and has won many recent official computer chess tournaments such as CCT 8 and 9, the 2006 Dutch Open Computer Championship, the 16th IPCCC, and the 15th World Computer Chess Championship. As of February 03, 2016, Stockfish is the top rated chess program on the IPON rating list.

Rank of a partition

In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this article is concerned, is that the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition. The concept was introduced by Freeman Dyson in a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition.

Definition

By a partition of a positive integer n we mean a finite multiset λ = { λ_k, λ_{k − 1}, . . . , λ₁ } of positive integers satisfying the following two conditions:

Cartan subalgebra

In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra of a Lie algebra that is self-normalising (if for all , then ). They were introduced by Élie Cartan in his doctoral thesis.

Existence and uniqueness

Cartan subalgebras exist for finite-dimensional Lie algebras whenever the base field is infinite. If the field is algebraically closed of characteristic 0 and the algebra is finite-dimensional then all Cartan subalgebras are conjugate under automorphisms of the Lie algebra, and in particular are all isomorphic.

Kac–Moody algebras and generalized Kac–Moody algebras also have Cartan subalgebras.

Properties

A Cartan subalgebra of a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic 0 is abelian and also has the following property of its adjoint representation: the weight eigenspaces of restricted to diagonalize the representation, and the eigenspace of the zero weight vector is . (So, the centralizer of coincides with .) The non-zero weights are called the roots, and the corresponding eigenspaces are called root spaces, and are all 1-dimensional.

Rank (formation)

A Rank is a line of military personnel, drawn up in line abreast (i.e. standing side by side).

Usage

Commonly, troops called to 'By the right, fall in!' do so by forming in line abreast, determining their initial position in relation to a marker. This may be a position on the ground or a single person placed previously to the movement. Often troops determine their spacing on the rank by extending their right arm to touch the left shoulder of the marker, or the person on that marked position, and, then starting from the right, align themselves visually to form a straight row. The alignment may then be checked by a non-commissioned officer making observations and calling orders from the end of the rank. (The order may be given to fall in by the left).

References

Bibliography