1,568 reputation
621
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location Kaiserslautern, Germany
age 27
visits member for 3 years, 10 months
seen 8 hours ago

I am a PhD student at the Algorithms & Complexity group at University of Kaiserslautern, Germany. I research design and analysis of parallel algorithms and data structures.

In my free time I read books, enjoy (and sometimes make) music, code, work out and roam the webs.


You can find sources for all self-created images I post on Stack Exchange here.


Aug
8
comment Question concerning a list sorting problem
Crossposted to cs.SE.
Aug
1
comment Why does convolution not maintain asymptotic equality of coefficients?
Hm, I note that $g$ does not seem to be algebraic; $[z^n]\frac{\mathrm{Li}_2(cz)}{cz} = \frac{c^n}{(n+1)^2}$. It may be worthwhile to investigate convolutions of only algebraic generating functions.
Jul
31
comment Do asymptotically equivalent coefficients survive convolution at least in Θ?
I was able to solve the issue in my special application case by 0) picking a simple $L_B$ (OGF $(1-dz)^{-1}$), 1) applying the definition of $\sim$ and $\lim$ subsequently and 2) choosing a generous $\varepsilon$ for the lower bound. We indeed have $\Theta$-equality of the convolution's coefficients in this case.
Jul
31
comment Lower bound for a relative of the central binomial coeff
Huh. In the partial fraction expansion the denominator $1-4z-z^2$ occurs which has that zero; apparently its contribution cancels out. My bad. Anyway, I don't see how to get to strict lower bounds from an asymptotic so asymptotic singularity analysis (at least as far as I know it) it out of the question.
Jul
31
awarded  Curious
Jul
30
comment Lower bound for a relative of the central binomial coeff
Since the dominant singularity is at $-2 + \sqrt{5}$ you have $T(2m,m) \sim (2+\sqrt{5})^n \cdot \dots$, so a(ny) lower bound of order $4^m$ from some moderately sized $m$ on seems likely, yes.
Jul
30
comment Do asymptotically equivalent coefficients survive convolution at least in Θ?
In my application, I have $\rho < 1$ (since the languages usually grow exponentially; the others are (probably) boring). If a proof is easier for $\rho = 1$ but extends to smaller $\rho$, go ahead. (I lack the knowledge/skill to see what impact that can have.)
Jul
30
revised Do asymptotically equivalent coefficients survive convolution at least in Θ?
added 30 characters in body
Jul
30
accepted Expectation of maximum of a function whose expectation is concave
Jul
30
comment Why does convolution not maintain asymptotic equality of coefficients?
Since this goes well beyond the question as posed, I decided to write up the follow-up question as per your gut feeling. Thanks for thinking about this!
Jul
30
asked Do asymptotically equivalent coefficients survive convolution at least in Θ?
Jul
30
accepted Why does convolution not maintain asymptotic equality of coefficients?
Jul
29
revised Why does convolution not maintain asymptotic equality of coefficients?
added 120 characters in body
Jul
29
asked Why does convolution not maintain asymptotic equality of coefficients?
Jul
22
revised Two conversions to base three yield different results
Better title, tags and language.
Jul
22
comment Two conversions to base three yield different results
Yes, you are. (Please lay out the calculations in your own words and with the build-in formatting (Markdown + LaTeX).)
Jul
22
suggested suggested edit on Two conversions to base three yield different results
May
5
comment How to compute the pdf of a sum of iid random variable using discrete Fourier transform?
The "characteristic function" is also called moment generating function; wait, what is the $i$ doing there? In any case, this is a pure mathematics question without any apparent connection to CS, so I'm migrating it over to Mathematics.
Apr
25
comment Resources/Books for Discrete Mathematics
@imu96 That would depend on that person's aptitude and the high school, I guess. From what I can tell from the table of contents and some spot checks, basic familiarity with mathematical notation should be sufficient, so I'd say yes. The later chapters (in particular chapter 7, Generating Functions) may require a bit more (e.g. real analysis for chapter 7).
Apr
25
comment Is this BNF grammar ambiguous?
If I read your non-standard notation correctly, 1) is a left-derivation and 2) a right-derivation. Hence, this is not a witness for the grammar being ambiguous.