Questions tagged [cyclic-orders]

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7 votes
3 answers
474 views

Existence of a homogeneous cyclic order for arbitrary infinite cardinals

It seems striking that the cardinalities of $\aleph_0$ and $\mathfrak c = 2^{\aleph_0}$ each admit what I will call a "homogeneous cyclic order", via the examples of $ℚ/ℤ$ and $ℝ/ℤ$. By ...
Daniel Asimov's user avatar
1 vote
0 answers
71 views

Compatibility with multiplication of a cyclic order on a ring

I am copying my question from here: https://math.stackexchange.com/q/3233462/427611. Is it correct that $\mathbb Z/3\mathbb Z$ and $\mathbb Z/4\mathbb Z$ are the only rings with three or more ...
Alex C's user avatar
  • 133
-1 votes
1 answer
96 views

Card dealing mathematics problem [closed]

I have found the following card trick: Take a stack of n cards, with a known order. Deal the cards from your hand onto the table like this: Card from the top, then card from the bottom, from the top, ...
Frans van Rijn's user avatar
5 votes
1 answer
146 views

Weights on cyclic orderings

Are there standard or known weights/metrics on cyclic orders? Cyclic orderings are different ways of listing elements from a finite set, where you call two lists the same if they differ only by a ...
Niles's user avatar
  • 599
9 votes
1 answer
585 views

What kind of category is a cyclically ordered set?

Background: A preorder is a binary relation $\leq$ which is reflexive and transitive. We can write the transitive property as ${\leq}(a,b)\wedge{\leq}(b,c)\to{\leq}(a,c)$. There are additional axioms ...
Chris Culter's user avatar