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There is a natural partial order on partitions given by inclusion of Young diagrams. This partially ordered set is known as Young's lattice . The lattice was originally defined in the context of representation theory , where it is used to describe the irreducible representations of symmetric groups S n for all n , together with their branching ...
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.
We call a sequence of X's and Y's dominating if, reading from left to right, the number of X's is always strictly greater than the number of Y's. The cycle lemma [ 13 ] states that any sequence of m {\displaystyle m} X's and n {\displaystyle n} Y's, where m > n {\displaystyle m>n} , has precisely m − n {\displaystyle m-n} dominating circular ...
The ring of integers O K is a finitely-generated Z-module.Indeed, it is a free Z-module, and thus has an integral basis, that is a basis b 1, ..., b n ∈ O K of the Q-vector space K such that each element x in O K can be uniquely represented as