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arXiv · 1508.00318

Four Variations on Graded Posets

Yan X. Zhang
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Abstract

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.

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Yan X. Zhang. 2015-08-04. Four Variations on Graded Posets. https://arxiv.org/abs/1508.00318

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