We present the proof of the cyclic sieving conjectures for generalised non-crossing partitions associated to well-generated complex reflection groups due to Armstrong, respectively to Bessis and Reiner, for the 26 exceptional well-generated complex reflection groups. The computational details are provided in the manuscript “Cyclic sieving for generalised non-crossing partitions associated to co...

Sieving is essential in different number theoretical algorithms. Sieving with large primes violates locality of memory access, thus degrading performance. Our suggestion on how to tackle this problem is to use cyclic data structures in combination with in-place bucket-sort. We present our results on the implementation of the sieve of Eratosthenes, using these ideas, which show that this approac...

Assuming that there exist (infinitely many) Siegel zeros, we show the (Rosser–)Jurkat–Richert bounds in linear sieve cannot be improved, and similarly look at Iwaniec’s lower bound on Jacobsthal’s problem, as well minor improvements to Bru

Two-dimensional (2D) materials with atomic thickness and extraordinary physicochemical properties exhibit unique mass transport behaviors, enabling them as emerging nanobuilding blocks for separation membranes. Engineering 2D materials into membrane with subnanometer apertures for precise molecular sieving remains a great challenge. Here, we report rational-designing external forces to precisel...

The quantum sieving effect of H2/D2 at 77 K on commercially available carbon molecular sieves (1.5GN-H and 3KT-172) was studied. An exceptional reverse kinetic quantum effect is observed on 1.5GN-H where D2 diffuses much faster than H2 with a ratio of up to 5.83 at low pressure, and the difference is still very evident even as the pressure increases up to 1 bar. D2 also diffuses faster than H2 ...

We show cyclic sieving phenomena on annular noncrossing permutations with given cycle types. We define annular q-Kreweras numbers, annular q-Narayana numbers, and annular q-Catalan numbers, and show that a sum of annular q-Kreweras numbers becomes an annular q-Narayana number and a sum of annular q-Narayana numbers becomes an annular q-Catalan number. We also show that these polynomials are clo...