Block-factor denominator

Determine which intervening block weights contribute factors to the reduced denominator of F_ω(t) for every anchored composition ω, and prove that the denominator is a product of factors Φ_{B_j}(t) selected from those block weights, with the resulting Euler-characteristic support eventually a finite union of arithmetic progressions.

Background

For many anchored compositions, the enumerator has a denominator given by a single factor associated with a block weight. Other examples have multiple factors and multiple arithmetic progressions of nonzero Euler characteristics.

The conjecture proposes a general denominator shape, but the rule selecting the contributing block weights is explicitly unresolved. Repeated poles would explain polynomial growth of the Euler characteristics.