Apparent molar property: Difference between revisions

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uniform notation for molar vol
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In mathematics, the '''Chinese monoid''' is a [[monoid]] generated by a totally ordered alphabet with the relations ''cba'' = ''cab'' = ''bca'' for every ''a'' ≤ ''b'' ≤ ''c''. An [[algorithm]] similar to [[Craige Schensted|Schensted's]] algorithm yields characterisation of the equivalence classes and a [[cross-section theorem]]. It was discovered by {{harvtxt|Duchamp|Krob|1994}} during their classification of monoids with growth similar to that of the [[plactic monoid]], and studied in detail by Julien Cassaigne, Marc Espie, Daniel Krob, Jean-Christophe Novelli, and Florent Hivert in 2001.<ref>{{Citation |last1=Cassaigne |first1=Julien |last2=Espie |first2=Marc |last3=Krob |first3=Daniel |last4=Novelli |first4=Jean-Christophe |last5=Hivert |first5=Florent | title=The Chinese monoid |url=http://www.worldscinet.com/ijac/11/1103/S0218196701000425.html | doi=10.1142/S0218196701000425 | mr=1847182 | zbl=1024.20046 | year=2001 | journal=International Journal of Algebra and Computation | issn=0218-1967 | volume=11 | issue=3 | pages=301–334}}</ref> 
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The Chinese monoid has a [[regular language]] cross-section
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:<math> a^* \ (ba)^*b^* \ (ca)^*(cb)^* c^* \cdots \ </math>
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and hence polynomial growth of dimension <math>\frac{n(n+1)}{2}</math>.<ref>{{citation | last1=Jaszuńska | first1=Joanna | last2=Okniński | first2=Jan | title=Structure of Chinese algebras. | zbl=1246.16022 | journal=J. Algebra | volume=346 | number=1 | pages=31–81 | issn=0021-8693 | arxiv=1009.5847 | url=http://arxiv.org/abs/1009.5847v2 | year=2011 }}</ref>
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==References==
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{{reflist}}
* {{Citation | last1=Duchamp | first1=Gérard | last2=Krob | first2=Daniel | title=Words, languages and combinatorics, II (Kyoto, 1992) | publisher=World Sci. Publ., River Edge, NJ | mr=1351284 | zbl=0875.68720 | year=1994 | chapter=Plactic-growth-like monoids | pages=124–142 |url=http://www.liafa.jussieu.fr/web9/rapportrech/description_en.php?idrapportrech=487}}


[[Category:Combinatorics]]
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[[Category:Semigroup theory]]


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{{combin-stub}}
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{{abstract-algebra-stub}}

Revision as of 01:28, 28 February 2014

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