B. Richmond and A. Knopfmacher . Compositions with distinct parts. Aequationes Math. , 49:86-97, 1995. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Measures of Distinctness for Random Partitions and Compositions .. - Hwang, Yeh (1997) (4 citations) (Correct)
....The corresponding problems for compositions are, unlike most other ones, more complicated and first treated by Knopfmacher and Mays [31, 32] They derived some combinatorial properties of the number and sum of distinct parts using an elementary approach. Another paper by Richmond and Knopfmacher [44] is also interesting since the results there further reveal the intricacy of the composition structure when studied from a distinct viewpoint. See also Warlimont [51] for a multiplicative counterpart. A closely related stochastic model to integer composition is the one studied by Chen [9] There ....
L. B. Richmond and A. Knopfmacher. Compositions with distinct parts. Aequationes Mathematicae 49 (1995) 86--97.
Limit Theorems for the Number of Summands in Integer Partitions - Hwang (1997) (2 citations) (Correct)
....(cf. 1, Ch. 11] For tail behaviors of the number of summands in general partitions, see [20] Finally, our auxiliary results on the functions Q and Y and the methods of proof of Theorem 3 is useful in giving a more (analytic) partition theoretic proof of the results by Richmond and Knopfmacher [32] concerning the number of compositions with distinct parts; this problem will be studied elsewhere. ....
L. B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae, 49 (1995), 86--97.
Measures of Distinctness for Random Partitions and Compositions .. - Hwang, Yeh (1997) (4 citations) (Correct)
....The corresponding problems for compositions are, unlike most other ones, more complicated and first treated by Knopfmacher and Mays [31, 32] They derived some combinatorial properties of the number and sum of distinct parts using an elementary approach. Another paper by Richmond and Knopfmacher [44] is also interesting since the results there further reveal the intricacy of the composition structure when studied from a distinct viewpoint. See also Warlimont [51] for a multiplicative counterpart. A closely related stochastic model to integer composition is the one studied by Chen [9] There ....
L. B. Richmond and A. Knopfmacher. Compositions with distinct parts. Aequationes Mathematicae 49 (1995) 86--97.
Compositions With Parts Constrained By The - Leading Summand Arnold Self-citation (Knopfmacher) (Correct)
....a composition of n. It is well known that there are 2 compositions of n. Composition counting problems become more interesting when constraints relating to the parts a i or their relative order are introduced. For example, in [2] compositions with no two adjacent equal parts are studied, and in [5] compositions with all parts distinct are considered. Binary compositions (all parts powers of two) are treated in [3] Of course, the best known class of compositions are those with nonincreasing parts, better known as partitions of n) We consider here compositions of the natural number n for ....
B. Richmond and A. Knopfmacher . Compositions with distinct parts. Aequationes Math. , 49:86-97, 1995.
The Sum Of Distinct Parts In Compositions And Partitions - Knopfmacher, Mays (1998) (2 citations) Self-citation (Knopfmacher) (Correct)
....formulas and asymptotic estimates for the mean values of F and G. Partitions and compositions are often studied by making restrictions on the nature of the parts, so that for instance one might consider partitions into parts 2 or 3 (mod 5) or compositions into distinct parts as analyzed in [5]. A second type of restriction is on the number of parts, such as partitions into at most k parts, or compositions in which at least one part of size l occurs (enumerated with the function C l (n) below) Wilf in [6] considers a di erent statistic: the number of di erent sizes of parts in a ....
.... as tabulated is a weighted sum, given by l F (n; l) This is the appropriate measure to use for a mean value of the sum of distinct parts, since it represents sum l occurring with frequence F (n; l) The main diagonal of Table 1 enumerates compositions into distinct parts, as studied in [5]. There is an obvious pattern to the entries of the rst two columns of the table. The next two results give combinatorial interpretations for columns 3 and 4, and then we provide a more general generating function approach. 0 ; otherwise. Proof. The sum of distinct parts can be 3 only ....
B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae 49 (1995), 86-97.
Compositions with m Distinct Parts - Knopfmacher, Mays (1996) (4 citations) Self-citation (Knopfmacher) (Correct)
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B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae 49 (1995), 86-97.
Limit Theorems for the Number of Summands in Integer Partitions - Hwang (2000) (2 citations) (Correct)
No context found.
L. B. Richmond and A. Knopfmacher, Compositions with distinct parts, Aequationes Mathematicae, 49 (1995), 86--97.
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