It is shown that, at low temperatures up to the ambiant one, it is possible to replace the actual inexplicit distribution function of the fractional exclusion statistics by an equivalent explicit one whose form does not change with the parameter α. But this alternative simpler distribution function given by a generalization of Pauli exclusion principle from the level of the maximal occupation number is not completely equivalent to the distributions obtained from the level of state number counting of the fractional exclusion particles. PACS: 05.30.-d,05.30.Pr,05.20.-y The principle of the fractional exclusion statistics (FES) was for the first time proposed about 60 years ago by Gentile[1] who suggested an intermediate maximum occupation number changing from 1 (for fermions) to ∞ (for bosons). This idea was later recognized and developed in the study of anyons and quasi-particle excitations for some low dimensional systems relevant t
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