Combinatorics of Polytopes

Subpolytopes of Cyclic Polytopes

✍ Tibor Bisztriczky; Gyula Károlyi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 85 KB

A remarkable result of Shemer [7] states that the combinatorial structure of a neighbourly 2mpolytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic 2m-polytope is cyclic. In this note, we present a direct proof of this co

Fiber Polytopes for the Projections betw

Fiber Polytopes for the Projections between Cyclic Polytopes

✍ Christos A. Athanasiadis; Jesús A. De Loera; Victor Reiner; Francisco Santos 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 359 KB

The cyclic polytope C (n, d) is the convex hull of any n points on the moment curve {(t, t 2 , . . . , t d ) : we consider the fiber polytope (in the sense of Billera and Sturmfels [6]) associated to the natural projection of cyclic polytopes π : C(n, d ) → C(n, d) which 'forgets' the last dd coord

Combinatorics of Determinantal Ideals

📂 Fiction 📅 2006 🏛 Nova Science Publishers 🌐 English ⚖ 76 KB

Combinatorics of Free Cumulants

✍ Bernadette Krawczyk; Roland Speicher 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 282 KB

We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about R-diagonal elements. Our inv

Cyclic coloration of 3-polytopes

✍ Michael D. Plummer; Bjarne Toft 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 418 KB

A cyclic coloration of a planar graph G is an assignment of colors to the points of G such that for any face bounding cycle the points of f have different colors. We observe that the upper bound 2p\*(G), due to 0. Ore and M. D. Plummer, can be improved to p \* ( G ) + 9 when G is 3connected (p\* den

A class of Hamiltonian polytopes

✍ P. R. Goodey 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 208 KB

## Abstract It is shown that any simple 3‐polytope, all of whose faces are triangles or hexagons, admits a hamiltonian circuit.