scholarly journals Four-generated direct powers of partition lattices and authentication

2021 ◽  
Vol 99 (3-4) ◽  
pp. 447-472
Author(s):  
Gabor Czedli
Keyword(s):  
Partition Lattices

Algebraic Aspects of Partition Lattices

1992 ◽  
pp. 106-122 ◽  
Author(s):  
Ivan Rival ◽  
Miriam Stanford
Keyword(s):  
Partition Lattices

scholarly journals Chains, antichains, and complements in infinite partition lattices

2018 ◽  
Vol 79 (2) ◽  
Author(s):  
James Emil Avery ◽  
Jean-Yves Moyen ◽  
Pavel Růžička ◽  
Jakob Grue Simonsen
Keyword(s):  
Partition Lattices

Noise Barriers with 2-D Partition Lattices

2003 ◽  
Vol 43 (5) ◽  
pp. 722-726
Author(s):  
Sung Soo Jung ◽  
Seung Il Cho ◽  
Yong Bong Lee ◽  
Woo Seop Lee
Keyword(s):  
Noise Barriers ◽  
Partition Lattices

scholarly journals Cumulants and partition lattices II: generalised k-statistics

1986 ◽  
Vol 40 (1) ◽  
pp. 34-53 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Asymptotic Behaviour ◽  
Random Variables ◽  
Möbius Function ◽  
Mobius Function ◽  
Joint Cumulants ◽  
Partition Lattices

AbstractThe role played by the Möbius function of the lattice of all partitions of a set in the theory of k-statistics and their generalisations is pointer out and the main results conscerning these statistics are drived. The definitions and formulae for the expansion of products of generalished k-statistics are presented from this viewpoint and applied to arrays of random variables whos moments satisfy stitable symmentry constraints. Applications of the theory are given including the calculation of (joint) cumulants of k-statistics, the minimum variace estimation of (generalised) moments and the asymptotic behaviour of generalised k-statistics viewed as (reversed) martingales.

scholarly journals Cumulants and partition lattices III: Multiply-indexed arrays

1986 ◽  
Vol 40 (2) ◽  
pp. 161-182 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Random Variables ◽  
Unbiased Estimation ◽  
Linear Combinations ◽  
Components Of Variance ◽  
Partition Lattices ◽  
Special Case

AbstractEarlier work of the author exploiting the role of partition lattices and their Mbius functions in the theory of cumulants, k-statistics and their generalisations is extended to multiply-indexed arrays of random variables. The natural generalisations of cumulants and k-statistics to this context are shown to include components of variance and the associated linear combinations of mean-squares which are used to estimate them. Expressions for the generalised cumulants of arrays built up as sums of independent arrays of effects as in anova models are derived in terms of the generalized cumulants of the effects. The special case of degree two, covering the unbiased estimation of components of variance, is discussed in some detail.

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