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This note introduces a code snippet in R aiming to generate necklaces as well as bracelets. Among various uses, necklaces are useful tools to manage traces of products of random matrices. Functionality for necklaces and bracelets is provided with some examples of applications such as Lyndon words and de Bruijn sequences. The routines are collected in the Necklaces package available from the Comprehensive R Archive Network.

Multivariate subordinated L\'evy processes are widely employed in finance for modeling multivariate asset returns. We propose to exploit non-linear dependence among financial assets through multivariate cumulants of these processes, for which we provide a closed form formula by using the multi-index generalized Bell polynomials. Using multivariate cumulants, we perform a sensitivity analysis, to investigate non-linear dependence as a function of the model parameters driving the dependence structure

Through the classical umbral calculus, we provide a 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, taking into account the Doubilet approach to symmetric functions. Moreover, by using exponential polynomials rather than set partitions, we provide a new formula for $k$-statistics that results in a very fast algorithm to generate such estimators., Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6163 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)