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Cumulants, free cumulants and half-shuffles [PDF]
Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often ...
Kurusch Ebrahimi-Fard +1 more
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13 pages; minor changes and ...
Hayato Saigo
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On the Combinatorics of Cumulants [PDF]
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Gian-Carlo Rota, Jianhong Shen
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The author considers binary sequences (i.e. having letters from the set \(\{0,1\})\), and defines binary cumulants for joint probability distributions on binary sequences of finite length. Distributions on binary sequences of finite length are related to solve some fundamental mathematical problems (e.g. Hilbert's 17th problem).
Torney, David C.
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37 pages, 27 ...
Yannis Pantazis +4 more
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Cumulative Subtraction Games [PDF]
We study a variation of Nim-type subtraction games, called Cumulative Subtraction (CS). Two players alternate in removing pebbles out of a joint pile, and their actions add or remove points to a common score. We prove that the zero-sum outcome in optimal play of a CS with a finite number of possible actions is eventually periodic, with period $2s ...
Gal Cohensius +3 more
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Giovanni Pistone, Henry P. Wynn
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Cumulate and Cumulative Granites and Associated Rocks [PDF]
Abstract. Processes that move crystals relative to melt, that is crystal fractionation, are of major importance in producing variations that are observed within cogenetic suites of granites. In low‐temperature granite suites, crystal fractionation initially involves the progressive separation of crystals residual from partial melting from that partial
Bruce W. Chappell, Doone Wyborn
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