Catherine Stenson

Relationships Among Flag f -Vector Inequalities for Polytopes

Abstract We examine linear inequalities satisfied by the flag

Families of Tight Inequalities for Polytopes

f

Let π Be a Function

-vectors of polytopes. One source of these inequalities is the toric

Tiling a (2 × n)-Board with Squares and Dominoes

g

Graphs and Surfaces

-vector; convolutions of its entries are non-negative for rational polytopes. We prove a conjecture of Meisinger about a redundancy in these inequalities. Another source of inequalities is the {\bf cd}-index; among all

Appendix C: Permutations

d

Appendix B: A Brief Survey of Groups

-polytopes, each {\bf cd}-index coefficient is minimized on the

Knots and Links

d

Appendix D: Modular Arithmetic

-simplex. We show that not all of the {\bf cd}-index inequalities are implied by the toric

Appendix E: Solutions and Hints to Selected Exercises

g