Mallows and Shapiro, (J. Integer Sequences 2 (1999)) have recently considered what they dubbed the problem of balls on the lawn. Our object is to explore a natural generalization, the s-tennis ball problem, which reduces to that considered by Mallows and Shapiro in the case s = 2. We show how this generalization is connected with s-ary trees, and employ the notion of generating trees to obtain a solution expressed in terms of generating functions.
THE TENNIS BALL PROBLEM / D. MERLINI; R. SPRUGNOLI; M. VERRI. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - STAMPA. - 99:(2002), pp. 307-344. [10.1006/jcta.2002.3273]
THE TENNIS BALL PROBLEM
MERLINI, DONATELLA;SPRUGNOLI, RENZO;VERRI, MARIA CECILIA
2002
Abstract
Mallows and Shapiro, (J. Integer Sequences 2 (1999)) have recently considered what they dubbed the problem of balls on the lawn. Our object is to explore a natural generalization, the s-tennis ball problem, which reduces to that considered by Mallows and Shapiro in the case s = 2. We show how this generalization is connected with s-ary trees, and employ the notion of generating trees to obtain a solution expressed in terms of generating functions.File | Dimensione | Formato | |
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