Mark Mixer
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View article: Reflexible covers of prisms
Reflexible covers of prisms Open
The Tomotope provided the first well understood example of an abstract 4-polytope whose connection (monodromy) group was not a string C-group, and which also did not have a unique minimal regular cover. Conversely, we know that if the conn…
View article: Bridging Theory and Practice: Building an Inclusive Undergraduate Data-Science Program
Bridging Theory and Practice: Building an Inclusive Undergraduate Data-Science Program Open
As the field of data science continues to evolve, institutions of higher education face the challenge of developing curricula that prepare students for the industry's rapidly changing landscape. In this paper, we will present a case study …
View article: Work in Progress: A Structural Change in Calculus Sequences
Work in Progress: A Structural Change in Calculus Sequences Open
At Wentworth Institute of Technology, more than two-thirds of students take calculus. Recently, 37% of those students were unsuccessful in their calculus courses. This impedes degree progress and impacts retention rates. Data suggests stud…
View article: Conditional probability of derangements and fixed points
Conditional probability of derangements and fixed points Open
The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the conditional probability that the $(k+1)^{st}$ point is fixed, gi…
View article: Conditional Probability of Derangements and Fixed Points
Conditional Probability of Derangements and Fixed Points Open
The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the conditional probability that the $(k+1)^{st}$ point is fixed, gi…
View article: Archimedean toroidal maps and their minimal almost regular covers
Archimedean toroidal maps and their minimal almost regular covers Open
The automorphism group of a map acts naturally on its flags (triples of incident vertices, edges, and faces). An Archimedean map on the torus is called almost regular if it has as few flag orbits as possible for its type; for example, a ma…
View article: The ranks of alternating string C-groups
The ranks of alternating string C-groups Open
In this paper, string C-groups of all ranks $3 \leq r \leq \frac{n}{2}$ are provided for each alternating group $A_n$, $n \geq 12$. As the string C-group representations of $A_n$ have also been classified for $n \leq 11$, and it is known t…
View article: Highest rank of a polytope for An
Highest rank of a polytope for An Open
We prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n = 5; 4 if n = 9; 5 if n = 10; 6 if n = 11; and the floor of of (n-1)/2 if n>=12. Moreover, if n = 3; 4; 6; 7 or 8, the group An is not a …
View article: Internal and external duality in abstract polytopes
Internal and external duality in abstract polytopes Open
We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then, …
View article: An extension of the classification of high rank regular polytopes
An extension of the classification of high rank regular polytopes Open
Up to isomorphism and duality, there are exactly two non-degenerate abstract regular polytopes of rank greater than $n-3$, one of rank $n-1$ and one of rank $n-2$, with automorphism groups that are transitive permutation groups of degree $…
View article: Internal and external duality in abstract polytopes
Internal and external duality in abstract polytopes Open
We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then, …
View article: Internal and external duality in abstract polytopes
Internal and external duality in abstract polytopes Open
We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then, …
View article: Cubic Tessellations of the Helicosms
Cubic Tessellations of the Helicosms Open
Up to isomorphism there are six fixed-point free crystallographic groups in Euclidean Space generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of E3 by such a group. The cubic tessellati…