Various ways of counting Young tableaux have been explored and lead to the definition of and identities for Schur functions.
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Predrag Cvitanović, Group Theory: Birdtracks, Lie's, and Exceptional Groups.
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Since the former convention is mainly used by Anglophones while the latter is often preferred by Francophones, it is customary to refer to these conventions respectively as the English notation and the French notation; for instance, in his book on symmetric functions, Macdonald advises readers preferring the French convention to "read this book upside down in a mirror" (Macdonald 1979, p.2).
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