Words coding set partitions
نویسندگان
چکیده
منابع مشابه
Set partitions as geometric words
Using an analytic method, we derive an alternative formula for the probability that a geometrically distributed word of length n possesses the restricted growth property. Equating our result with a previously known formula yields an algebraic identity involving alternating sums of binomial coefficients via a probabilistic argument. In addition, we consider refinements of our formula obtained by...
متن کاملSet partitions, words, and approximate counting with black holes
Words satisfying the restricted growth property wk ≤ 1 + max{w0, . . . , wk−1} are in correspondence with set partitions. Underlying the geometric distribution to the letters, these words are enumerated with respect to the largest letter occurring, which corresponds to the number of blocks in the set partition. It turns out that on average, this parameter behaves like log1/q n, where q is the p...
متن کاملLimit Behavior of Maxima in Geometric Words representing Set Partitions
We consider geometric words ω1 · · ·ωn with letters satisfying the restricted growth property ωk ≤ d + max{ω0, . . . , ωk−1}, where ω0 := 0 and d ≥ 1. For d = 1 these words are in 1-to-1 correspondence with set partitions and for this case we show that the number of left-to-right maxima (suitable centered) does not converge to a fixed limit law as n tends to infinity. This becomes wrong for d ≥...
متن کاملCoding Partitions
Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD), we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the “unique decipherability” at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the c...
متن کاملOn Partitions Separating Words
Partitions {Lk}k=1 of A + into m pairwise disjoint languages L1, L2, . . . , Lm such that Lk = L + k for k = 1, 2, . . . , m are considered. It is proved that such a closed partition of A+ can separate the words u1, u2, . . . , um ∈ A+ (i.e. each Lk contains exactly one word of the sequence u1, u2, . . . , um) if and only if for each pair i, j of distinct elements in {1, 2, . . . , m}, the word...
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ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2011
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm110205005o