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Multiple consecutive runs of multi-state trials: distributions of patterns
Yong Kong
The pattern is defined to have at least consecutive 's followed by at least consecutive 's, , followed by at least con…
Distributions of successions of arbitrary multisets
Yong Kong
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successi…
Joint distribution of rises, falls, and number of runs in random sequences
Yong Kong
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of th…
The m-th Longest Runs of Multivariate Random Sequences
Yong Kong
The distributions of the -th longest runs of multivariate random sequences are considered. For random sequences made up of kinds of letters, the lengths of the runs are sort…