Hello, fellow colleagues in the Julia community. This question may not be a good fit for the Julia Discourse, but any help is appreciated. I was exploring Analytic Combinatorics (by Flajolet & Sedgewick). The part about binary words (words over a binary alphabet). contains the following generating…

I fixed it thanks to RicBit . W_n<k,k> notation stands for [z^n] Taylor(W<k,k>). That is, we need the 200th coefficient of the Taylor expansion of W<k,k>. This version works: function n_words(r;n_tot=200) coefs = collect(series(w_rr(r,z),z,0,n_tot+1),z) coefs.coeff(z,n_tot) end function p…

Maybe Rational{BigInt}(1/(2^n)) doesn’t give the expected result, as the 2 in 2^n is parsed as an Int64 and when raised to 200 gives 0 (i.e. zero(Int)) making the whole expression 1//0. The intended value can be obtained with 1/BigInt(2)^200: julia> Rational{BigInt}(1/(2^200)) # bad result 1//0 j…

Thank you! It worked like a charm. Do you have any idea about my 2nd and 3rd questions?

This is nice, but I don’t think using SymPy is really using Julia :wink: Maybe GitHub - JuliaDiff/TaylorSeries.jl: Taylor polynomial expansions in one and several independent variables. can help. (Disclaimer: I am one of the co-authors.)

I gave it a shot, but it seems that there’s something wrong with the types again. The results are blowing up. using TaylorSeries w_rr(r,z) = (1-z^(r+1))/(1-2z+z^(r+1)) n_words(r;n_tot=200) = getcoeff(taylor_expand(z -> w_rr(z,r),order=n_tot+1),n_tot) function p_k(k,n) #a = FastRational{Int1…

Late update: This turned into a full package for analytic combinatorics [image] GitHub - fargolo/AnalyticComb.jl: Solutions for combinatorial problems using... Solutions for combinatorial problems using symbolic methods. and applications for time-seri…

Yes, @Datseris ! I will take a look at the link. Thank you.

Another update: [image] Combinatorial time-loops: probabilistic inference on time-series based on... Recurrence quantification analysis (RQA) is inspired by Poincaré’s early studies and describes non-linear characteristics of dynamical systems. It achieves this by identifying similaritie…

Trying Julia for Analytic combinatorics

General Usage

Datseris March 12, 2026, 1:28pm 8

Interesting! WOuld you be interested in giving a talk at an upcoming JuliaDynamics monthly meeting about this?

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Trying Julia for Analytic combinatorics

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