507- Problem list (III)

For Part II, see here.

(Many thanks to Robert Balmer, Nick Davidson, and Amy Griffin for help with this list.)

• The Erdös-Turán conjecture on additive bases of order 2.
• If is the -th Ramsey number, does exist?
• Hindman’s problem: Is it the case that for every finite coloring of the positive integers, there are and such that , , , and are all of the same color?
• Does the polynomial Hirsch conjecture hold?
• Does ? (See also this post (in Spanish) by Javier Moreno.)
• Mahler’s conjecture on convex bodies.
• Nathanson’s conjecture: Is it true that for “almost all” finite sets of integers ?
• The (bounded) Burnside’s problem: For which is the free group finite?
• Is the frequency of 1s in the Kolakoski sequence asymptotically equal to ? (And related problems.)
• A question on Narayana numbers: Find a combinatorial interpretation of identity 6.C7(d) in Stanley’s “Catalan addendum” to Enumerative combinatorics.

Part IV.

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