159 research outputs found

    Some Ramsey theorems for finite nn-colorable and nn-chromatic graphs

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    Given a fixed integer nn, we prove Ramsey-type theorems for the classes of all finite ordered nn-colorable graphs, finite nn-colorable graphs, finite ordered nn-chromatic graphs, and finite nn-chromatic graphs.Comment: 7 page

    Symmetries and Ramsey properties of trees

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    AbstractIn this paper we show the extent to which a finite tree of fixed height is a Ramsey object in the class of trees of the same height can be measured by its symmetry group

    Four Variations on Graded Posets

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    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
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