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1: 17.12 Bailey Pairs
Weak Bailey Lemma
2: 26.14 Permutations: Order Notation
A weak excedance is a position j for which σ ( j ) j . …It is also equal to the number of permutations in 𝔖 n with exactly k + 1 weak excedances. …
3: 14.19 Toroidal (or Ring) Functions
14.19.2 P ν - 1 2 μ ( cosh ξ ) = Γ ( 1 2 - μ ) π 1 / 2 ( 1 - e - 2 ξ ) μ e ( ν + ( 1 / 2 ) ) ξ F ( 1 2 - μ , 1 2 + ν - μ ; 1 - 2 μ ; 1 - e - 2 ξ ) , μ 1 2 , 3 2 , 5 2 , .
4: Bibliography
  • G. E. Andrews (1979) Plane partitions. III. The weak Macdonald conjecture. Invent. Math. 53 (3), pp. 193–225.
  • 5: 26.12 Plane Partitions
    A strict shifted plane partition is an arrangement of the parts in a partition so that each row is indented one space from the previous row and there is weak decrease across rows and strict decrease down columns. …
    6: Errata
  • Equation (14.19.2)
    14.19.2 P ν - 1 2 μ ( cosh ξ ) = Γ ( 1 2 - μ ) π 1 / 2 ( 1 - e - 2 ξ ) μ e ( ν + ( 1 / 2 ) ) ξ F ( 1 2 - μ , 1 2 + ν - μ ; 1 - 2 μ ; 1 - e - 2 ξ ) , μ 1 2 , 3 2 , 5 2 ,

    Originally the argument to F in this equation was incorrect ( e - 2 ξ , rather than 1 - e - 2 ξ ), and the condition on μ was too weak ( μ 1 2 , rather than μ 1 2 , 3 2 , 5 2 , ). Also, the factor multiplying F was rewritten to clarify the poles; originally it was Γ ( 1 - 2 μ ) 2 2 μ Γ ( 1 - μ ) ( 1 - e - 2 ξ ) μ e ( ν + ( 1 / 2 ) ) ξ .

    Reported 2010-11-02 by Alvaro Valenzuela.