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Monoid of all words in the alphabet of positive integers modulo Knuth equivalence
In mathematics, the plactic monoid is the monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified
Plactic_monoid
Algebraic structure with an associative operation and an identity element
bicyclic monoid, and ⟨ a , b | a b a = b a a , b b a = b a b ⟩ {\displaystyle \langle a,b\,\vert \;aba=baa,bba=bab\rangle } is the plactic monoid of degree
Monoid
q_{s}=0} . Plactic monoid Cassaigne, Julien; Espie, Marc; Krob, Daniel; Novelli, Jean-Christophe; Hivert, Florent (2001), "The Chinese monoid", International
Chinese_monoid
bicyclic monoid, and ⟨ a , b | a b a = b a a , b b a = b a b ⟩ {\displaystyle \langle a,b\,\vert \;aba=baa,bba=bab\rangle } is the plactic monoid of degree
Presentation_of_a_monoid
American computer scientist and mathematician (born 1938)
Fisher–Yates shuffle Robinson–Schensted–Knuth correspondence Man or boy test Plactic monoid Quater-imaginary base Triangular number The Complexity of Songs Uniform
Donald_Knuth
French mathematician (1920–1996)
Schützenberger is credited with the foundation of the notion of the plactic monoid, reflected in the name of the combinatorial structure called by some
Marcel-Paul_Schützenberger
Computer science problem
technique for finding the length of the longest increasing subsequence Plactic monoid − an algebraic system defined by transformations that preserve the length
Longest increasing subsequence
Longest_increasing_subsequence
Bijective correspondence in mathematics
which provides a diagrammatic interpretation of the correspondence. Plactic monoid: the insertion process can be used to define an associative product
Robinson–Schensted correspondence
Robinson–Schensted_correspondence
Combinatorial object in representation theory
all semistandard Young tableaux, giving it the structure called the plactic monoid (French: le monoïde plaxique). In representation theory, standard Young
Young_tableau
French mathematician
and Grothendieck polynomials, as well as novel terminology like the plactic monoid and vexillary permutations. They were also the first to define the crystal
Alain_Lascoux
Type of group in abstract algebra
representations provide a rich source of problems involving Young tableaux, plactic monoids, and the Bruhat order. Subgroups of symmetric groups are called permutation
Symmetric_group
Mathematics concept
{\displaystyle y=x} -axis, and this precisely switches the roles of P and Q. Plactic monoid Jeu de taquin Bruce E. Sagan. The Symmetric Group. Springer, 2001.
Viennot's geometric construction
Viennot's_geometric_construction
PLACTIC MONOID
PLACTIC MONOID
Boy/Male
Egyptian
Name of a pharaoh.
Girl/Female
Muslim/Islamic
Sunnah practice
Boy/Male
Hindu
To practice
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Placid
Girl/Female
Indian, Telugu
Practice
Girl/Female
Indian, Punjabi, Sikh
Practice
Girl/Female
Indian
Placid
Boy/Male
Tamil
Placid
Boy/Male
Sikh
Practice
Boy/Male
Tamil
Sankeerth | ஸஂகிரà¯à®¤
To practice
Sankeerth | ஸஂகிரà¯à®¤
Girl/Female
Muslim
Sunnah, Practice
Boy/Male
Indian, Sanskrit
Practice
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Placid
Boy/Male
Hindu, Indian
Practice; Study
Girl/Female
Arabic, Muslim
Sunnah; Practice
Boy/Male
Indian
Practice
Boy/Male
Muslim
Practice or garden
Boy/Male
Arabic, Bengali, Hindu, Indian, Kashmiri, Muslim, Tamil
Practice
Girl/Female
Hindu, Indian
Practice
Male
English
English name derived from Latin Placidus, PLACID means "calm, placid."
PLACTIC MONOID
PLACTIC MONOID
Girl/Female
German
Pledge; Hostage
Girl/Female
Indian
Ray of hope
Boy/Male
Tamil
A significant particle
Girl/Female
Christian & English(British/American/Australian)
The Bee
Boy/Male
Indian, Sanskrit
Blessing of the Gods
Biblical
recompense of God; camel of God
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Strong; Coral
Girl/Female
Hindi
Radiant.
Girl/Female
English Irish
meaning a rhythmic flow of sounds.
Female
Icelandic
Feminine form of Icelandic Páll, PÃLA means "small."
PLACTIC MONOID
PLACTIC MONOID
PLACTIC MONOID
PLACTIC MONOID
PLACTIC MONOID
v. i.
To perform certain acts frequently or customarily, either for instruction, profit, or amusement; as, to practice with the broadsword or with the rifle; to practice on the piano.
n.
Any fish having placoid scales, as the sharks.
a.
Pertaining to what may be taken apart; as, clastic anatomy (of models).
n.
Frequently repeated or customary action; habitual performance; a succession of acts of a similar kind; usage; habit; custom; as, the practice of rising early; the practice of making regular entries of accounts; the practice of daily exercise.
a.
Of or pertaining to milk; procured from sour milk or whey; as, lactic acid; lactic fermentation, etc.
a.
Not plastic or easily molded.
a.
Of or pertaining to milk; got from milk; as, galactic acid.
n.
Systematic exercise for instruction or discipline; as, the troops are called out for practice; she neglected practice in music.
v. t.
To exercise one's self in, for instruction or improvement, or to acquire discipline or dexterity; as, to practice gunnery; to practice music.
n.
a substance composed predominantly of a synthetic organic high polymer capable of being cast or molded; many varieties of plastic are used to produce articles of commerce (after 1900). [MW10 gives origin of word as 1905]
a.
Able to return quickly to a former state or condition, after being depressed or overtaxed; having power to recover easily from shocks and trials; as, elastic spirits; an elastic constitution.
n.
Application of science to the wants of men; the exercise of any profession; professional business; as, the practice of medicine or law; a large or lucrative practice.
v. t.
To do or perform frequently, customarily, or habitually; to make a practice of; as, to practice gaming.
n.
Practice.
a.
Fragmental; made up of brok/ fragments; as, sandstone is a clastic rock.
a.
Springing back; having a power or inherent property of returning to the form from which a substance is bent, drawn, pressed, or twisted; springy; having the power of rebounding; as, a bow is elastic; the air is elastic; India rubber is elastic.
v. t.
To teach or accustom by practice; to train.
a.
Capable of being molded, formed, or modeled, as clay or plaster; -- used also figuratively; as, the plastic mind of a child.
v. i.
To learn by practice; to form a habit.
a.
Having the power to give form or fashion to a mass of matter; as, the plastic hand of the Creator.