ACTA issues

On associative spectra of operations

Sebastian Liebscher, Tamás Waldhauser

Acta Sci. Math. (Szeged) 75:3-4(2009), 433-456

Abstract. The distance of an operation from being associative can be ``measured'' by its associative spectrum, an appropriate sequence of positive integers. Associative spectra were introduced in a publication by B. Csákány and T. Waldhauser in 2000 for binary operations (see [CsakanyWaldhauser]). We generalize this concept to $2 \le p$-ary operations, interpret associative spectra in terms of equational theories, and use this interpretation to find a characterization of fine spectra, to construct polynomial associative spectra, and to show that there are continuum many different spectra. Furthermore, an equivalent representation of bracketings is studied.

AMS Subject Classification (1991): 08B05, 08B15, 08A62, 05C05

Keyword(s): associative spectrum, bracketing, term operation, equational theory, tree, Catalan numbers

Received September 1, 2008. (Registered under 6422/2009.)