(Λ₁, ..., Λ_n)-permanents and systems of bounded representatives

Abstract

The aim of this paper is to show that the l/n expansion for n-photon processes can be considered as a quasiclassical one. We discuss qualitatively the domain of validity of the leading term of this expansion and show how corrections to it can be accounted for in a systematic and univocal way. Applications to photoionisation processes in strong laser or microwave fields are also discussed.

Modern enumeration theory of permutations with restricted positions

“…In [13] Mine obtained the more general result for any α, β, 7 G C, and the author in [14] proved the simpler formula 1 -1, if nEEO(mod6), 0, if η = 1,5 (mod 6), 2, if η = 2,4 (mod 6), 3, if η ΞΞ 3 (mod 6), following from (5) and the recurrence Mine formula [13] for per(a/ n + β Ρ + 7 P 2 ), is found by the author in [19]. In [14] and [20] the author obtained some different representations for per (a/ n + β Ρ + -/Ρ 2 + δ Ρ 3 ) and per (al n + βΡ + ^Ρ 2 + δ Ρ 3 + εΡ 4 ) by the composition method and the method of coefficients. The detailed information about the combinatorial identities connected with these representations see in [21].…”

“…(2) Z «l lap 2 M oreover using the results of Bolshakov [3,4],and Bebiano [5], we show [77] that the enumeration of r-permutations of n elements (with repetitions) with restricted positions, which is connected with the enumeration of permutations of multisets [6, p. 33] with the corresponding restrictions on positions of elements, can be reduced to the enumeration of η-permutations with restricted positions.…”