The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a finite set, C be a finite cyclic group acting on X , and f(q) be a polynomial in q with nonnegative integer coefficients. Then the triple (X,C, f(q)) exhibits the cyclic sieving phenomenon if, for all g ∈ C, we have #X = f(ω) where # denotes cardinality, X is the fixed point set of g, and ω is a ...

Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain codes. For example, it is shown that, among dual Hamming codes over Fq, generating function for codedwords according to major index statistic (resp. inversion statistic) gives rise CSP when q=2 or q=3 q=2). A byproduct curious characterization irreducible polynomials F2[x] and F3[x] that are ...

Let Pn denote the poset of matchings on 2n points on a circle, labeled 1, 2, . . . , 2n in cyclic order, in which we define an element to be less than another element if it can be obtained by an uncrossing. Let Pn,k denote the level of the poset with k crossings. Let Pn,k denote the level of the poset with k crossings. We study the cyclic sieving phenomenon of Pn,k. It is known that the triple ...

A compact mesh architecture for supporting the relation collection step of the number field sieve is described. Differing from TWIRL, only isolated chips without inter-chip communication are used. According to a preliminary analysis for 768-bit numbers, with a 0.13 μm process one mesh-based device fits on a single chip of ≈(4.9 cm)—the largest proposed chips in the TWIRL cluster for 768-bit occ...

We describe a hardware device for supporting the sieving step in integer factoring algorithms like the quadratic sieve or the number field sieve. In analogy to Bernstein’s proposal for speeding up the linear algebra step, we rely on a mesh of very simple processing units. Manufacturing the device at moderate cost with current hardware technology on standard wafers with 200 mm or 300 mm diameter...

Molecular sieving MFI-type zeolite membranes were prepared by a secondary growth method without using an organic template. Silicalite membranes with intercrystalline pores minimized or eliminated were obtained by this synthesis method which avoids the template removal step. The silicalite membrane exhibits molecular sieving characteristics with pervaporation separation factor for p-xylene to o-...

The operational function of the trunk limbs (thoracic appendages), Daphnia, P3 and P4, is a long-term disputed definition between “solid walls”, sieving filters. Sieving unlikely process for routine particle collection, capture not simple mechanical by alone. Analysis promotion supported direct observational examination in-vivo cinematographic slow-motion film magnified solid photos tethered Da...

In the agroindustry, sieving is a unit operation of great value, this work aims to make literature review on in cereals, search equation was carried out Scopus database with keywords sieve, screen, food process, and cereal that resulted 132 articles 174 patents. Of articles, 44 were directly related 14 more had something do sieving; patents, last 10 years only 7 sieving. To find new trends, raw...

For a positive integer k, the Erdös-Selfridge function is the least integer g(k) > k + 1 such that all prime factors of (g(k) k ) exceed k. This paper describes a rapid method of tabulating g(k) using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of g(k). A table of values of g(...