The Hilbert series F̃μ of the Garsia-Haiman module Mμ can be described combinatorially as the generating function of certain fillings of the Ferrers diagram of μ where μ is an integer partition of n. Since there are n! fillings that generate F̃μ, it is desirable to find recursions to reduce the number of fillings that need to be considered when computing F̃μ combinatorially. In this paper, we pres...

We present a depth-first search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in the Bron–Kerbosch algorithm. All the maximal cliques generated are output in a tree-like form. Subsequently, we prove that its worst-case time complexity is O(3n/3) for an n-vertex graph. This is optimal as a function of n, since there exist up to 3n/3...

Background & Aims: Shift work is programmed in various schedules, each has its own advantages and disadvantages. The main purposes of this study were: a) to determine common shift schedules used in petrochemical industries, b) to compare shift work health-related problems among employees working in different shift schedules and c) to recommend appropriate shift schedule. Methods: This cross...

Let n be a positive integer and t non-zero integer. We consider the two-parameter family of elliptic curves over $$\mathbb {Q}$$ given by $$\begin{aligned} \mathcal {E}_n(t):y^2=x^3+tx^2-n^2(t+3n^2)x+n^6. \end{aligned}$$ prove result non-divisibility point $$(0,n^3) \in {E}_n(t)(\mathbb {Q})$$ whenever is sufficiently large compared to $$t^2+3n^2t+9n^4$$ squarefree. Our work extends this previo...

Effects of final state interaction on asymmetries in inclusive scattering of polarized electrons on polarized He are investigated using a consistent He bound state wave function and 3N continuum scattering states. Significant effects are found, which influence the extraction of the magnetic neutron form factor from AT8 . The enhancement found experimentally for ATL8 near the 3N breakup threshol...

1,2,4,5-Tetram ethylim idazole (3) is obtained by m etalation o f 2,4,5-trim ethylim idazole (2) with sodium in liquid am m onia and subsequent addition o f methyl iodide. 3 reacts w ith Lewis acids to form the com pounds M e4C 3N 2 BH3 (8) and M e4C 3N 2-E + (4, 5, 7, 10; E = Me, H, SiM e3, C(O)M e). The X-ray structure reveals the ionic nature o f pentam ethylim idazolium iodide (4) in the so...

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...