Hankel matrices consisting of Catalan numbers have been analyzed by various authors. Desainte-Catherine and Viennot found their determinant to be $\prod_{1 \leq i \leq j \leq k} {{i+j+2n}\over {i+j}}$ and related them to the Bender - Knuth conjecture. The similar determinant formula $\prod_{1 \leq i \leq j \leq k} {{i+j-1+2n}\over {i+j-1}}$ can be shown to hold for Hankel matrices whose entries are successive middle binomial coefficients ${{2m+1} \choose m}$. Generalizing the Catalan numbers in a different direction, it can be shown that determinants of Hankel matrices consisting of numbers ${{1}\over {3m+1}} {{3m+1} \choose m}$ yield an alternate expression of two Mills – Robbins – Rumsey determinants important in the enumeration of plane partitions and alternating sign matrices. Hankel matrices with determinant 1 were studied by Aigner in the definition of Catalan – like numbers. The well - known relation of Hankel matrices to orthogonal polynomials further yields a combinatorial application of the famous Berlekamp – Massey algorithm in Coding Theory, which can be applied in order to calculate the coefficients in the three – term recurrence of the family of orthogonal polynomials related to the sequence of Hankel matrices.

A splitting of an additive Abelian group G is a pair (M; S), where M is a set of integers and S is a subset of G such that every nonzero element g 2 G can be uniquely written as m h for some m 2 M and h 2 S. Splittings of groups by the set M = f 1; : : :; kg are intimately related to tilings of the n{ dimensional Euclidean space. Further, such a splitting corresponds to a perfect shift code used in the analysis of run{length limited codes correcting single peak shifts. We shall give the structure of the splitting set S for splittings of cyclic groups Z p of prime order by sets of the form M = f1; a

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The purpose of this paper is to analyze the effects of organizational formalization on the behavioral, market, product, and process types of firm innovativeness as well as the interplay between these different innovativeness types. Based on data collected through a survey of the financial services industry in Turkey, the analyses show that formalization directly hinders both behavioral and market innovativeness. Moreover, as behavioral innovativeness influences product and process innovativeness, formalization's effect on these types of innovativeness are indirect. As expected, the study also finds that process innovativeness facilitates both product and market innovativeness and that product innovativeness foster market innovativeness. This study makes a contribution to the literature by examining the linkages between formalization in firms and the various firm innovativeness types, which have previously been studied only separately. The study thus provides a richer understanding of the relationship between formalization and firm innovativeness types.

A general construction for perfect integer codes is provided, which allows to efficiently compute such codes. The method is applied to investigate in detail the special special error set {±1, ±a, ±b, ±c, } interesting for single error correction of peak shifts and codes defined on lattices.