Marko Riedel's Combinatorics Links

• Egorychev method
• Combinatorial math at MSE

Wikipedia

Papers

• MSc thesis MRiedel (PDF)
• MSc thesis MRiedel (PS.GZ)

Polya's enumeration theorem and the symbolic method. PDF compressed file. (180K) collier.pdf

Measuring post-quickselect disorder. With Alois Panholzer and Helmut Prodinger. (275K) PDF file. qsdis-jalc.pdf

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)

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)

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