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The Pfaffian transform.

Austin, Tracale, Bantilan, Hans, Egge, Eric S., Jonas, Isao, Kory, Paul (2009)

Journal of Integer Sequences [electronic only]

The ratio and generating function of cogrowth coefficients of finitely generated groups

Ryszard Szwarc (1998)

Studia Mathematica

Let G be a group generated by r elements g 1 , , g r . Among the reduced words in g 1 , , g r of length n some, say γ n , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of γ 2 n has a limit, called the cogrowth exponent with respect to the generators g 1 , , g r . We show by analytic methods that the numbers γ n vary regularly, i.e. the ratio γ 2 n + 2 / γ 2 n is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated...

The reciprocal super Catalan matrix

Helmut Prodinger (2015)

Special Matrices

The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.

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