| Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties and patterns. As in other experimental sciences, experimental mathematics can be used to make mathematical predictions which can then be verified or falsified on the bases of additional computational experiments.; In this thesis, we apply computer technology to three problems: (1) Discovering and proving Symmetric Chain Decompositions for Young's Lattices L (3, n) and L(4, n); (2) Making Extensions of the Goulden-Jackson Cluster method; (3) Finding and proving additive periods for the Sprague-Grundy function of Wythoff's game. |
