## Basic PosetsThis book introduces the reader to the general theory of partially ordered sets, i.e., posets. The text is presented in a rather informal manner, with interesting examples and computations, which rely on the Hasse diagram to build graphical intuition for the structure of finite posets. The proofs of a small number of theorems is included in the appendix. Important examples especially the Letter N poset, which plays a role akin to that of the Petersen graph in providing a candidate counterexample to many propositions, are used repeatedly throughout the text. |

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### Contents

How to Represent a Poset | 7 |

Poset Morphisms | 42 |

Construction of New Posets | 61 |

Connectedness | 95 |

Linear Extensions | 113 |

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### Common terms and phrases

adjacency matrix angle order antichain bijective binary relation chain C4 chain of order circle order conclude connected poset Consider a poset consider the poset constant map construct count the number cover preserving Define a map definition denote the number draw the Hasse example finite poset formula full subposet given poset graph Harris isomorphism Hasse diagram hence image f(X interval order Let f letter N poset lexicographic order Li(X line segments linear extensions map g maximal chain means minimal elements N-free natural labeled posets natural number number of line one-to-one order preserving order geometry order ideals order preserving mapping ordinal sum partially ordered set paths of length point Xj poset as follows poset with Hasse poset X poset XY product order product poset Proof representation polynomial semiorder series-parallel Similarly singleton straight lines subset Suppose Theorem underlying set universally connected XY is connected XY)z