Marko Riedel's homepage

Recommended posts from Math Stackexchange

This is the best-of list. The page has my papers on the Egorychev method, the functional equation of the Riemann Zeta Function, and on Coupon Collector type problems with EGFs and Stirling numbers.

Papers

Functional equation of the Riemann Zeta function

• Mellin transform and the functional equation of the Riemann Zeta function (PDF)
and here:
• Mellin transform and the functional equation of the Riemann Zeta function (PS.GZ)

Coupon collector and Stirling numbers

• Coupon collector and Stirling numbers (PDF)
and here:
• Coupon collector and Stirling numbers (PS.GZ)

Exponential formula and subset / multiset sums

• Cycle indices from the exponential formula and subset / multiset sums (PDF)
and here:
• Cycle indices from the exponential formula and subset / multiset sums (PS.GZ)

OEIS Wiki

My Master's Thesis

PDF file. (1.4M) msc-thesis-riedel-extr.pdf

Conjectures

• Nested Cycle Partitions have on average

  $\theta(\sqrt{n})$ components: ncp-comp2.pdf

  OEIS A392471

• The cycle index of the toroidal group on $n\times k$

  slots only depends on $\gcd(n,k)$ and $n\times k$

  (integer factorizations under toroidal symmetry): toroidal.pdf

  OEIS A392445

• Given that a permutation has cycle set $[m]$ for some $m$

  the expected value of $m$ is on average $\theta(\sqrt{n})$

  dcs-statA.pdf

  OEIS A393036

• The number of cycles in a permutation whose cycle set

  is $[m]$ for some $m$ is on average $\theta(\sqrt{n})$

  dcs-statB.pdf

  OEIS A392215

Torus transform and torus numbers (generalized Stirling numbers)

• Torus transform and its inverse

  ts3-inv.pdf

  OEIS A394559

• Torus numbers: the number of tori in a random set partition

  into 3-tori is on average $\theta(\log^3(n))$

  torus-ts3.pdf

  OEIS A393519

• Torus numbers: the number of tori in a random set partition

  into ordinary tori is on average $\theta(\log^2(n))$

  torus-ts.pdf

  OEIS A338805

Playing Sudokus