Combinatorics

Date: Aug 2, 2010

FPSAC 2010

I'm currently happy attendant of FPSAC 2010 (formal power series & algebraic combinatorics) in San Francisco. My talk on random walks in the plane has been the very first regular one, which means that I can now fully enjoy all the other ones. read more »

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randomwalks-fpsac2010.pdf
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Date: Mar 5, 2010

Computer proved monotonicity of some coefficients

Ming-Hua Lin from the University of Regina sent me the following problem:

Problem: Let p ≥ 2 be an integer, and define

$$ f (t) = \left( \frac{1}{1 - t \left( \frac{1}{p} + \frac{p - 1}{2 p^2} t<br /> \right)} \right)^p = \sum_{n \geqslant 0} c_n t^n . $$

Show that $ c_2 > c_3 > c_4 > \cdots $. read more »

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Date: Aug 18, 2009

CARMA workshop in Newcastle, 2009

On August 18, 2009, the University of Newcastle hosted a CARMA workshop on Multidimensional Numerical Integration and Special Function Evaluation. Besides enjoying very interesting talks it's been my pleasure to present, together with James Wan, on progress of our joint work with Jon Borwein, Peter Donovan and Dirk Nuyens on expectations of random walks. read more »

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randomwalkintegrals.pdf
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Date: Jun 10, 2009

Fast q-binomials in Mathematica

Recently, I have been doing experiments involving q-binomial coefficients in Mathematica. Starting with version 7, Mathematica is prepared for some q-business; in particular, there exists a function named QBinomial giving the q-analog of Binomial. However, this implementation turned out to not be fast enough for my needs. Here is an alternative approach which is not only way faster but provides a full factorization. read more »

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Date: Apr 23, 2007

Eulerian numbers

This short introduction to Eulerian numbers accompanied my talk for the WZ Theory class held by Tewodros Amdeberhan at Tulane University in Spring 2007. read more »

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euleriannumbers.pdf
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euleriannumbers-presentation.pdf
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