/**
 * Shared combinatorics for the simplicial polytope builders' authoring range.
 *
 * The ordering contract these helpers implement is frozen (P55B Part B):
 * `(k+1)`-subsets enumerate lexicographically over ascending indices, and a
 * combinatorial explosion refuses arithmetically — by name, with the
 * offending numbers — before a single element is allocated.
 */
/** `C(n, k)` as a float, capped: returns `Infinity` once it exceeds 2^53. */
export declare function binomial(n: number, k: number): number;
/** Refuses a group whose index total exceeds the budget, before allocating. */
export declare function assertGroupWithinBudget(builder: string, cellDim: number, cellCount: number, verticesPerCell: number): void;
/**
 * All `size`-subsets of `0…n-1`, lexicographic, ascending within a subset —
 * exactly the order the builders' historical nested loops produced, which is
 * why the default groups stay byte-identical through this generalization.
 */
export declare function lexicographicSubsets(n: number, size: number): Uint32Array;
/** Shared input validation: a safe integer dimension and a finite positive size. */
export declare function assertBuilderInputs(builder: string, dim: number, sizeName: string, size: number): void;
/** Validates an explicit `maxCellDimension` against the builder's range. */
export declare function assertMaxCellDimension(builder: string, requested: number, highest: number, highestReason: string): void;
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