A combinatorial solution of two related problems in sequence enumeration

AbstractThis paper gives a combinatorial derivation of the counting series ψm (alternatively ψm∗) for positive integer sequences by rises, falls and levels (alternately exceedances, deficiencies and constants)

Families of bosonic suppression laws beyond the permutation symmetry principle

Exact cancellation of quantum amplitudes in multiphoton interferences with Fock states at input, the so-called suppression or zero transmission laws generalizing the Hong-Ou-Mandel dip, are useful tool in quantum information and computation. It was recently suggested that all bosonic suppression laws follow from a common permutation symmetry in the input quantum state and the unitary matrix of interferometer. By using the recurrence relations for interference of Fock states, we find a wealth of suppression laws on the beamsplitter and tritter which are not explained by the permutation symmetry principle. Our results reveal that in interference with Fock states on unitary multiports there are whole families of suppression laws for arbitrary total number of bosons even on asymmetric unitary multiports, beyond the previously formulated permutation symmetry principle.Comment: 19 pages, 3 figure