Some Explorations on Two Conjectures About Rademacher Sequences

Some Conjectures About Cyclotomic Integers

Some Results on Two Conjectures of Schützenberger

We present some partial results surrounding two conjectures of Schützenberger on evacuations of Young tableaux.

Some Conjectures about Integral Means Of

1. The problems. In this note we shall discuss some conjectural integral inequalities which are related to quasiconformal mappings, singular integrals, martingales and the calculus of variations.

On Some Conjectures about Arithmetic Partial Differential Equations

In this paper, we study the arithmetic partial differential equations x′p = ax n and x ′ p = a. We solve a conjecture of Haukkanen, Merikoski, and Tossavainen (HMT, in short) about the number of solutions (conjectured to be finite) of the equation x ′ p = ax n and improve a theorem of HMT about finding the solutions of the same equation. Furthermore, we also improve another theorem of HMT about...

Confirming Two Conjectures About the Integer Partitions

For a given integer n, let 4n denote the set of all integer partitions *1 *2 } } } *m>0 (m 1), of n. For the dominance order ``P'' on 4n , we show that if two partitions *, + are both chosen from 4n uniformly at random, and independent of each other, then Pr(*P+) 0 as n . This statement answers affirmatively a question posed by Macdonald in 1979. The proof is based on the limit joint distributi...