## Tagged Questions

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### A family of words counted by the Catalan numbers

In recent work with Michael Albert and Nik Ruškuc, a family of words has arisen which is counted by the Catalan numbers. I've looked at Richard Stanley's Catalan exercises in EC2 a …
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### Can the fact that the square of an integer is a natural number be categorified?

If $a$ and $b$ are natural numbers, then $a-b$ is an integer and so the square $(a-b)^2$ is a natural number. In particular $$(a-b)^2 \geq 0. \qquad (1)$$ Combining this fact …
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### Can one bound the Quadratic Points on Curves?

Let $C$ be a nonsingular projective curve defined over $\mathbb{Q}$, which does not admit a map of degree 1 or 2 to $\mathbb{P}^1$ or to an elliptic curve. It is then a consequence …
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### probability measures with entropy equal to nonnegative number

Is it true that for a given nonnegative number, there exists a measure-theoretical entropy value (supremum of entropies of all partitions under a measure-preserving transformation) …
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### homology class of a rational curve

Let $X\subseteq\mathbb{C}P^n$ be s smooth variety. Let $C\subseteq X$ be an algebraic rational curve [i.e. an algebraic curve which is birational to $\mathbb{C}P^1$]. In what fol …
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