L. Carlitz. Restricted compositions. Fibonacci Quarterly, 14:254-264, 1976. Home/Search Document Not in Database Summary Related Articles Check |
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Distinctness of compositions of an integer: A Probabilistic.. - Hitczenko, Louchard (2001) (Correct)
.... u w j 2 u u Y i=1 1 e e L( w i ) e e L( w i ) Pr(Dn m) F ( with F ( P 1 0 f( i) Figure 6 shows the limiting (discrete) probability distribution of Dn , f( together with the numerical estimation of f (circle) 4 Carlitz Compositions The Carlitz compositions ([7]) are characterized by the property that two successive parts are di erent. In this section, we rst analyze the hitting probability to a large part value. This allows us to derive the asymptotics for the expected number of distinct part sizes of Carlitz composition, a result rst proved in [17] ....
Carlitz, L. Restricted Compositions, The Fibonacci Quart., 14, 254264, 1976.
Probabilistic Analysis of Carlitz Compositions - Guy Louchard And Self-citation (Carlitz) (Correct)
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L. Carlitz. Restricted compositions. Fibonacci Quarterly, 14:254-264, 1976.
On Carlitz Compositions - Knopfmacher, Prodinger (1998) Self-citation (Carlitz) (Correct)
....zeros allowed (correcting an erroneous formula from Carlitz) It is also briefly demonstrated that so called 1 compositions of a natural number can be treated in a similar style. October 14, 1997 1. Introduction A restricted composition of a natural number n in the sense of Carlitz [4], which we shall call a Carlitz composition, is defined to be a composition n = a 1 a 2 Delta Delta Delta a k such that a i 6= a i 1 for i = 1; k Gamma 1: We refer to n as the size and to k as the number of parts of the composition. Observe that there are 2 unrestricted ....
....i 1 for i = 1; k Gamma 1: We refer to n as the size and to k as the number of parts of the composition. Observe that there are 2 unrestricted compositions of the integer n with generating function 1= 1 Gamma z= 1 Gamma z) Let c(n) denote the number of Carlitz compositions of n. In [4], Carlitz found the generating function C(z) Since we are going to compute several related parameters we find it useful to rederive his result in a streamlined way, using a method that has appeared for example in [6] under the nickname adding a new slice. We proceed from a Carlitz ....
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L. Carlitz, Restricted Compositions, The Fibonacci Quarterly 14 (1976), 254--264.
Probabilistic Analysis of Carlitz Compositions - Louchard, Prodinger (1999) Self-citation (Carlitz) (Correct)
....the width and thickness of a composition. We finally present a typical simulation. The limiting processes are characterized by Brownian Motion and some discrete distributions. 1 Introduction A Carlitz composition of n is a composition two successive parts of which are different (see Carlitz [4]) T (m; n) will denote the number of Carlitz compositions of n with m parts. All T ( Delta; n) compositions will be considered as equiprobable. We call M the random variable (R.V. number of parts. In [12] Knopfmacher and Prodinger found asymptotic values for : T ( Delta; n) the mean number ....
CARLITZ, L., Restricted Compositions, The Fibonacci Quarterly, 14, 254-264, 1976.
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