## Small Dehn-Sommerville Spaces

Dehn-Sommerville spaces are generalized spheres as they share many properties of spheres: Euler characteristic and more generally Dehn-Sommerville symmetries.

Dehn-Sommerville spaces are generalized spheres as they share many properties of spheres: Euler characteristic and more generally Dehn-Sommerville symmetries.

We have calculated with graphs from the very beginning: Humans computed with pebbles like in this scene of the `Clan of the Cave Baer` (1986)) or with line graphs when writing with tally sticks (see this lecture). In all of these cases, the addition of graphs is the disjoint union which serves a nice monoid like the natural numbers. It … ….

The f-function of a graph minus 1 is the sum of the antiderivatives of the f-function anti-derivatives evaluated on the unit spheres.

Dehn-Sommerville relations are a symmetry for a class of geometries which are of Euclidean nature.

Branko Grünbaum (1929-2018) passed away last September. Here is the obituary from the university of Washington. One of his master pieces is the book “Tilings and patterns”, written with G.C. Shephard. The well illustrated book is considered the bible on Tilings. Here is a page from that book: Links: Personal website at Washington. croatia.org featuring an other picture. Wikipedia entry … ….

Some update about recent activities: a new calculus course, the Cartan magic formula and some programming about the coloring algorithm.

We prove that any discrete surface has an Eulerian edge refinement. For a 2-disk, an Eulerian edge refinement is possible if and only if the boundary length is divisible by 3

Anatole Katok, 1944-2018

We prove that connected combinatorial manifolds of positive dimension define finite simple graphs which are Hamiltonian.

About the origin of the definitino of shellability.