Abstract
The purpose of this paper is to investigate several context-free grammars suggested by the Lotka-Volterra system. Some combinatorial arrays, involving the Stirling numbers of the second kind and Eulerian numbers, are generated by these context-free grammars. In particular, we present grammatical characterization of some statistics on cyclically ordered partitions.
Highlights
The purpose of this paper is to investigate several context-free grammars suggested by the Lotka-Volterra system
Throughout this paper a context-free grammar is in the sense of Chen [4]: for an alphabet A, let Q[[A]] be the rational commutative ring of formal power series in monomials formed from letters in A
The Stirling number of the second kind n k is the number of ways to partition [n] into k blocks
Summary
Throughout this paper a context-free grammar is in the sense of Chen [4]: for an alphabet A, let Q[[A]] be the rational commutative ring of formal power series in monomials formed from letters in A. A context-free grammar over A is a function G : A → Q[[A]] that replace. The formal derivative D is a linear operator defined with respect to a context-free grammar G. A descent of a permutation π ∈ Sn is a position i such that π(i) > π(i + 1). Dt dt where y(t) and x(t) represent, respectively, the predator population and the prey population as functions of time, and a, b, c, d are positive constants. Motivated by (1), we shall consider context-free grammars of the form:. We present grammatical characterization of some statistics on cyclically ordered partitions
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