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165,976 questions
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Kollar-Mori's example of a flip
This question is reposted from SE, where I have not received an answer. I am happy to delete this if I get an answer there.
This question comes from Kollar-Mori's book Birational geometry of algebraic ...
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Vertex dominating circuits in cubic graphs
A well known conjecture asks about the existence of dominating circuits in cubic graphs, where a dominating circuit $C$ in a cubic graph $G$ is a circuit such that all edges in G have at least one ...
- 1,068
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Periodicity under $\mathbb{Z}$-graded stable equivalences
Let A and B be two finite dimensional selfinjective K-algebra (K a field) that are both $\mathbb{Z}$-graded. Assume that the stable category of finitely generated $\mathbb{Z}$-graded A-modules is ...
- 28.2k
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Lower bound on homomorphism density for a "sparse 2-blowup" of a graph
Definitions:
Let $H$ be a fixed bipartite graph and $G$ be an arbitrary graph. Let $t(H, G)$ denote the homomorphism density of $H$ in $G$:
$$ t(H, G) = \frac{|\mathrm{Hom}(H, G)|}{|V(G)|^{|V(H)|}} $$
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Closed form for A179382
Let
$a(n)$ be the smallest positive integer $m$ such that $(2n+1) \mid (2^m-1)$.
$b(n)$ be A179382, i.e., an integer sequence known as the smallest period of pseudo-arithmetic progression with ...
-1
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On the measure of the $\delta$-neighborhood of an orbit in ergodic automorphisms of the $d$-cube
Let $T: [0,1]^d \to [0,1]^d$ be an ergodic, measure-preserving automorphism. For an element $x \in [0,1]^d$, we define the $\delta$-neighborhood of its full orbit as:$$V_\delta(x) = \bigcup_{n \in \...
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Are two-step iterations of Knaster forcings Knaster?
A poset $\mathbb{P}$ is called $\kappa$-Knaster if every size-$\kappa$ subset of $\mathbb{P}$ has a size-$\kappa$ pairwise-compatible subset. This is therefore a strengthening of the $\kappa$-cc. One ...
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Does the image $\rho (G_{\mathbb{Q}_p})$ contain an open subgroup of $\mathbb Z_p^\times \cdot \mathrm{Id}$?
Let $G$ be a simple $p$-divisible group over $\mathbb{Z}_p$ (arising from a formal group over $\mathbb{Z}_p$, so connected), and let $V := T_p(G)\otimes_{\mathbb Z_p}\mathbb Q_p$
be its Tate module. ...
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Definition of category of analytic stacks
If I’m not mistaken, condensed mathematics is replacing the category of sets by condensed sets, so we can talk about topological objects up to homeomorphisms instead of (weak) homotopy equivalences.
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1
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Practicing probabilistic heuristics in additive analytic number theory
I am currently trying to understand the architecture of various proofs of results in additive analytic number theory. In particular, I am studying the proof that every large odd integer is the sum of ...
- 3,791
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43
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Relation between topologies on a set of Markov kernels
Let $X$ and $Y$ be Polish spaces and let $\mathcal{K}(X,Y)$ denote the set of Markov kernels from $(X,\mathcal{B}(X))$ to $(Y,\mathcal{B}(Y))$. Given $\mu\in \mathcal{P}(X)$ (the space of probability ...
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Floorplans for the Mondrian Art Puzzle
Let us say that a tiling of a square into rectangles is Mondrian if the rectangles (1) are pairwise non-congruent and (2) have the same area. It is an outstanding open problem whether there exists a ...
- 90k
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A conjecture on the sum of reciprocal exponents for $abc$-triples
1. Conjecture:
Based on empirical data and observations of results related to Diophantine equations of the form $a + b = c$, I propose the following conjecture:
Let $a, b, c$ be coprime positive ...
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Is there a $\lambda$-set on the real line that is not a $Q$-set?
Question:
In many ZFC models, there are $\lambda$-subsets of the real line that are not $Q$-sets. Does such an example exist in ZFC?
Background:
Recall that $X \subseteq \mathbb R$ is a $Q$-set if $X$ ...
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On pure rational numbers [duplicate]
In the literature is there a terminology for the following property of rational numbers;
A rational number in $\mathbb{Q}$ whose reduced form is in the form $\frac{p}{q}$ for two primes $p,q$.
By ...
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