The Wolfram Language has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original algorithms together with its high-level symbolic language has made it a unique environment for the exploration, development, and application of discrete mathematics.
RSolve — solve recurrence equations
FindSequenceFunction — find functions for integer sequences
ReplaceList — generate a list of forms matching a pattern
Graph — represent an undirected, directed, or mixed graph, or a multigraph
Groupings — generate all possible tree expressions from lists of elements
FindShortestTour — solve traveling salesman problems