Manuscript En02-E@2 · En02-E-v2.tex · section · c2769986

Phase-sensitive finite-state formulas

Deterministic flagged Fock approximation › Phase-sensitive finite-state formulas · lines 651–667

En02-E@2#eq:permanent

Let $T = K (I + K)^{- 1}$ . In the normalized occupation basis,

⟨ n ∣ ρ_{K} ∣ m ⟩ = {p_{0} per (T [n, m]) / \prod_{i} n_{i}! \prod_{i} m_{i}!, 0, ∣ n ∣ = ∣ m ∣, ∣ n ∣ \neq = ∣ m ∣.

The repeated-row and repeated-column matrix $T [n, m]$ contains row $i$ exactly $n_{i}$ times and column $i$ exactly $m_{i}$ times. The empty permanent is one.

Displayed formulas in this passage

En02-E@2#eq:permanent · line 654
$⟨ n ∣ ρ_{K} ∣ m ⟩ = {p_{0} per (T [n, m]) / \prod_{i} n_{i}! \prod_{i} m_{i}!, 0, ∣ n ∣ = ∣ m ∣, ∣ n ∣ \neq = ∣ m ∣.$

Nearby in this section

lemma: Lemma: Orientation-sensitive blocks and moments
section: Phase-sensitive finite-state formulas