More Restricted Growth Functions: Gray Codes and Exhaustive Generation

Abstract

International audienceA Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previous work, the authors of the present paper showed, among other things, that the m-ary Reflected Gray Code Order yields a Gray code for the set of restricted growth functions. Here we further investigate variations of this order relation, and give the first Gray codes and efficient generating algorithms for bounded restricted growth functions

Combinatorial Gray Codes — an Updated Survey

“…Sabri and Vajnovszki [SV17] consider Gray codes for set partitions with a fixed number of parts or an upper bound on the number of parts. They constructed a 5-Gray (in the RGS representation) for the first family and a 3-Gray code for the second family, based on sublists of generalizations of the BRGC, implying that both of these Gray codes are genlex; see Figure 12 (i3)-(i5).…”

On the exhaustive generation of generalized ballot sequences in lexicographic and Gray code order

“…Here we show that the restriction of the Reflected Gray Code to the sets of length n generalized and p-ary, with p even, ballot sequences induces a 3-adjacent Gray code. Similar techniques based on variations of the order relation induced by the Reflected Gray Code was used implicitly, for example in [5,19], and developed systematically as a general method in [1,11,12,[16][17][18], and our Gray codes are in the light of this direction. In the final part of this paper we give constant amortized time exhaustive generating algorithms for these classes of ballot sequences, in lexicographic order and for the corresponding Gray codes.…”