Combinatorial analysis of a combination scheme with restricted steps

Abstract

We introduce a new characteristic of the outcome of a combination scheme, i.e. its steps, defined as differences between the neighboring elements of the outcome arranged in the order of increase. We consider the procedure of enumerating all outcomes of a combination scheme with a given restriction, establish the one-toone correspondence between the outcomes and their numbers generated in the enumeration procedure, and give some methods to simulate the possible outcomes of the scheme.

Keywords

• combination scheme with restricted steps
• enumeration of outcomes
• enumeration problem
• simulation