A unifying framework for k-statistics, polykays and their multivariate generalizations
نویسنده
چکیده
Extending umbral methods introduced by Di Nardo and Senato (2006b), in this paper we provide an unifying syntax for single and multivariate k-statistics, polykays and multivariate polykays. From a combinatorial point of view, we revisit the theory as exposed by Stuart and Ord (1987) taking into account the Doubilet approach to symmetric functions. The Moebius function, occurring in the relations between bases of symmetric functions, is replaced by powers of a special umbra. Moreover suitable indexed umbrae allow a natural extension of k-statistics to multivariate case.
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