We determine the rank generating function, the zeta polynomial and the Möbius function for the poset NC(p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We give an alternative treatment of some of these results in the case q = 1, for which this poset is a lattice. We also consider the general case of multiannular non-crossing partitions of type B, and...

We consider non-standard matter effect in flavor conversion of neutrinos crossing the core of the Earth. We show that oscillation of core crossing neutrinos with E ∼ 0.5 GeV can be well described by a first order perturbation theory. We show that due to non-standard matter effect varying chemical composition in the Earth can modify the neutrino flavor conversion by 100%. Effects of CP violating...

PURPOSE To evaluate and compare the clinical and angiographic characteristics of retinal vein occlusion (RVO) in glaucomatous and non-glaucomatous eyes with unilateral RVO in the fellow eye. METHODS Twenty-one glaucomatous eyes (GL group) and 25 age-matched non-glaucomatous eyes (non-GL group) with unilateral RVO in the fellow eye were included in this study. Fluorescein angiographic images w...

A perfect straight-line matching M on a finite set P of points in the plane is a set of segments such that each point in P is an endpoint of exactly one segment. M is non-crossing if no two segments in M cross each other. Given a perfect straight-line matching M with at least one crossing, we can remove this crossing by a flip operation. The flip operation removes two crossing segments on a poi...

We consider $m$-divisible non-crossing partitions of $\{1,2,\ldots,mn\}$ with the property that for some $t\leq n$ no block contains more than one first $t$ integers. give a closed formula number multi-chains such prescribed blocks. Building on this result, we compute Chapoton's $M$-triangle in setting and conjecture combinatorial interpretation $H$-triangle. This is proved $m=1$.

A permutation pattern in which all letters within an occurrence are required to be adjacent is known as a subword. In this paper, we consider the distribution of several infinite families subword patterns on set non-crossing partitions size n, denoted by NCn, and derive formulas for generating functions these distributions NCn. As special cases our results, obtain enumerating members NCn accord...