278,723 research outputs found
Four Variations on Graded Posets
We explore the enumeration of some natural classes of graded posets,
including all graded posets, (2+2)- and (3+1)-avoiding graded posets,
(2+2)-avoiding graded posets, and (3+1)-avoiding graded posets. We obtain
enumerative and structural theorems for all of them. Along the way, we discuss
a situation when we can switch between enumeration of labeled and unlabeled
objects with ease, generalize a result of Postnikov and Stanley from the theory
of hyperplane arrangements, answer a question posed by Stanley, and see an old
result of Klarner in a new light.Comment: 28 page
The Impact of Sensing Range on Spatial-Temporal Opportunity
In this paper, we study the impact of secondary user (SU) sensing range on spectrum access opportunity in cognitive radio networks. We first derive a closed-form ex- pression of spectrum access opportunity by taking into ac- count the random variations in number, locations and trans- mitted powers of primary users (PUs). Then, we show how SU sensing range affects spectrum access opportunity, and the tradeoff between SU sensing range and spectrum ac- cess opportunity is formulated as an optimization problem to maximize spectrum access opportunity. Furthermore, we prove that there exists an optimal SU sensing range which yields the maximum spectrum access opportunity, and nu- merical results validate our theoretical analysis
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