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Formulae for well formed formulae and their enumeration

Published online by Cambridge University Press:  09 April 2009

Dov Tamari
Dov Tamari
Affiliation:
Department of Mathematics, State University of New York, at Buffalo, 4246 Ridge Lea Road, Amherst, N.Y. 14226, U.S.A.
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1. General Idea. In this paper formal operators and bracketings devices are essentially the same; so are well formed formulae and correct bracketings.

A well known theorem of symbolic logic (Post languages, etc.) and universal algebra characterizes well formed formulae among (linear) strings of symbols for variables and operators in terms of a system of numerical inequalities, one of them an equality.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 2 , March 1974 , pp. 154 - 162
Copyright
Copyright © Australian Mathematical Society 1974

References

[0]Cayley, A.: ‘On the analytical forms called trees’, 2nd part, Coll. Math. Papers, vol. 4, Cambride 1891, 114–5.Google Scholar
[1]Cohn, P. M.: Universal Algebra, (Harper and Row, 1965).Google Scholar
[2]Erdélyi, A. and Etherington, I. H. M.: ‘Some problems of non-associative combinations (2)’, Edinburgh Math. Notes, 32 (1940), VII–XII.CrossRefGoogle Scholar
[3] Fougères, D. de and Tamari, D.: ‘La structure polyèdrale des complexes de parenthésages’, (submitted).Google Scholar
[4]Knuth, Don: Fundamental Algorithms, (Addison-Wesley, 1969.)Google Scholar
[5]Raney, G. N.: ‘Functional composition patterns and power series reversion’, Trans. Amer. Math. Soc. 94 (1960), 441–51.CrossRefGoogle Scholar
[6]Rosenbloom, P. C.: The elements of mathematical logic. (Dover 1950.)Google Scholar
[7]Silberger, D. M.: ‘Occurence of the integer (2n–1)!/n! (n–1)!’; Prace Mat. 13 (1969), 91–96; M. R. 40 # 2556.Google Scholar
[8]Tamari, D.: Monoides préordonnés et chaînes de Malcev; Thèse, (Paris 1951) (printed part in Bull. Soc. Math. France 82 (1954), 53–96).Google Scholar
[9]Tamari, D., ‘The algebra of bracketings and their enumeration’, Nieuw Arch. Wisk. X (1962), 131–146.Google Scholar