5 citations · 8 across the 7 of their papers we have counts for
7 papers
A Discrete Four Vertex Theorem for Hyperbolic Polygons
Wiktor Mogilski, Kyle Grant
There are many four vertex type theorems appearing in the literature, coming in both smooth and discrete flavors. The most familiar of these is the classical theorem in differentia…
The -vector of a simplicial complex
Wayne A. Johnson, Wiktor J. Mogilski
We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, , and we introduce the -vector of $Δ…
Coxeter Groups, Ruins, and Weighted -cohomology
Wiktor Mogilski, Kevin Schreve
Given a Coxeter system and a multiparameter of real numbers indexed by , one can define the weighted -cohomology groups and associate to them a nonnega…
The weighted Singer conjecture for Coxeter groups in dimensions three and four
Wiktor J. Mogilski
Given a Coxeter system there is a contractible simplicial complex called the Davis complex on which acts properly and cocompactly. In an article of Dymara, the weig…
The fattened Davis complex and weighted -(co)homology of Coxeter groups
Wiktor J. Mogilski
Associated to a Coxeter system there is a contractible simplicial complex called the Davis complex on which acts properly and cocompactly by reflections. Given a po…
Polygon Vertex Extremality and Decomposition of Polygons
Wiktor J. Mogilski
In this paper, we show that if we decompose a polygon into two smaller polygons, then by comparing the number of extremal vertices in the original polygon versus the sum of the two…
The Four-Vertex Theorem, The Evolute, and The Decomposition of Polygons
Wiktor J. Mogilski
The Four-Vertex Theorem has been of interest ever since a discrete version appeared in 1813 due to Cauchy. Up until now, there have been many different versions of this theorem, bo…