Struct CycleIndexPolynomial 

pub struct CycleIndexPolynomial {
    pub group_name: String,
    pub terms: Vec<(u64, Vec<u32>)>,
    pub group_order: u64,
}

Represents the cycle index polynomial Z(G; x₁, …, xₙ) of a permutation group.

The cycle index is stored as a list of monomials, where each monomial is represented as a vector of exponents (e[i] = exponent of x_{i+1}).

Fields

group_name: String

Group name (for display).

terms: Vec<(u64, Vec<u32>)>

Each term: (coefficient, exponent_vector). The polynomial is (1/|G|) * ∑ coeff * ∏ x_i^{e_i}.

group_order: u64

Order of the group |G|.

Implementations

impl CycleIndexPolynomial

pub fn new(group_name: impl Into<String>, group_order: u64) -> Self

Create a new cycle index for a named group.

pub fn add_term(&mut self, coeff: u64, exponents: Vec<u32>)

Add a term to the cycle index.

pub fn eval_all_ones(&self) -> u64

Evaluate Z(G; 1, 1, …, 1) = |G| / |G| = 1 (should return 1).

pub fn burnside_count(&self, k: u64) -> u64

Apply Burnside’s lemma: the number of distinct colorings with k colors is Z(G; k, k, …, k).

Each term (coeff, exps) contributes coeff * ∏_i k^{exps[i]} = coeff * k^{∑ exps[i]}.

pub fn cyclic(n: u32) -> Self

The cycle index for C_n (cyclic group of order n).

Trait Implementations

impl Clone for CycleIndexPolynomial

fn clone(&self) -> CycleIndexPolynomial

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for CycleIndexPolynomial

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.