The monodromy group of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si49.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math>-pyramid

Berman, Leah Wrenn; Mixer, Mark; Monson, Barry; Oliveros, Déborah; Williams, Gordon

doi:10.1016/j.disc.2013.12.002

Cited by 5 publications

(7 citation statements)

References 8 publications

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“…4.12]. Describing the monodromy group of several families of polytopes is an active area of research; see [2,3,33,56,68].…”

Section: The Flag Actionmentioning

confidence: 99%

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Open problems on k-orbit polytopes

Cunningham

Pellicer

2018

Discrete Mathematics

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“…4.12]. Describing the monodromy group of several families of polytopes is an active area of research; see [2,3,33,56,68].…”

Section: The Flag Actionmentioning

confidence: 99%

“…Let {4, 4} [b,c] denote the underlying polytope of {4, 4} (b,c) . If P = {4, 4} [1,2] and Q = {4, 4} [1,4] , then both {4, 4} [6,7] and {4, 4} [2,9] are minimal covers of P and Q, neither of which covers the other.…”

Section: Mixingmentioning

confidence: 99%

Open problems on k-orbit polytopes

Cunningham

Pellicer

2018

Discrete Mathematics

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“…However, little is known about monodromy groups of non-regular polytopes. In the last decade, there has been an effort to understand these groups (see for example [2], [6], [12]). In particular in [6] Hartely et al study the monodromy group of the prism oven an n-gon and compute it, in terms of generators and relations.…”

Section: B Bmentioning

confidence: 99%

“…In particular in [6] Hartely et al study the monodromy group of the prism oven an n-gon and compute it, in terms of generators and relations. Moreover, in [2], Berman et al study that of the pyramid over an n-gon and show that it is an extension of the symmetric group S 4 by a cyclic group which sometimes splits (and determine when). We show that products of polytopes are useful to understand monodromy groups of some non-regular polytopes.…”

Section: B Bmentioning

confidence: 99%

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Products of abstract polytopes

Gleason

Hubard

2018

Journal of Combinatorial Theory, Series A

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Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological product, which also arises in a natural way. We show that these products have unique prime factorization theorems. We use this to compute the automorphism group of a product in terms of the automorphism groups of the factors and show that (non trivial) products are almost never regular or two-orbit polytopes. We finish the paper by studying the monodromy group of a product, show that such a group is always an extension of a symmetric group, and give some examples in which this extension splits. arXiv:1603.03585v1 [math.CO]• If P is the prism (or the bipyramid) over a 3-polytope having the property that all its vertex figures (faces) are isomorphic to an n-gon, with n not congruent to 0 modulo 9;• If = and each Q i has rank 2.By [2], we already know that the monodromy group of a pyramid over an n-gon is an extension of S 4 by (C m ) 4 , where m = p gcd (3,p) , and that such extension splits whenever n is not congruent to 0 modulo 9. Our techniques to show Theorem B can also be used to show this result. Abstract polytopesAbstract polytopes generalise the (face-lattice) of classical polytopes as combinatorial structures. In this chapter we review the basic theory of abstract polytopes and refer the reader to [11] for a detail exposition of the subject.An (abstract) n-polytope (or (abstract) polytope of rank n) P is a partially ordered set whose elements are called faces that satisfies the following properties. It contains a minimum face F −1 and a maximum

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Pyramids Over Regular 3-Tori

Pellicer¹,

Williams²

2018

SIAM J. Discrete Math.

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The monodromy group of then-pyramid

Cited by 5 publications

References 8 publications

Open problems on k-orbit polytopes

Open problems on k-orbit polytopes

Products of abstract polytopes

Pyramids Over Regular 3-Tori

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