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Given an odd prime number $p$ , we characterize the partitions $\underset{̲}{ℓ}$ of $p$ with $p$ non negative parts $ℓ_{0} \geq ℓ_{1} \geq ... \geq ℓ_{p - 1} \geq 0$ for which there exist permutations $σ, τ$ of the set ${0, ..., p - 1}$ such that $p$ divides $\sum_{i = 0}^{p - 1} i ℓ_{σ (i)}$ but does not divide $\sum_{i = 0}^{p - 1} i ℓ_{τ (i)}$ . This happens if and only if the maximal number of equal parts of $\underset{̲}{ℓ}$ is less than $p - 2$ . The question appeared when dealing with sums of $p$ -th powers of resolvents, in order to solve a Galois module structure problem.

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Parity indices of partitions

Parity of the partition function in arithmetic progressions.

Partially Ordered Sets and the Rogers-Ramanujan Identities.

Partition des nombres

Partition ideals of order 1, the Rogers-Ramanujan identities and computers

Partition identities. I: Sandwich theorems and logical 0-1 laws.

Partitioning multipartite numbers into a fixed number of parts which satisfy congruence conditions.

Partitions and indefinite quadratic forms.

Partitions excluding specific polygonal numbers as parts.

Partitions into K parts .

Partitions of natural numbers and their representation functions.

Partitions, q-Series and the Lusztig-Macdonald-Wall Conjectures.

Partitions with designated summands

Partitions with numbers in their gaps

Partitions with parts in a finite set and with parts outside a finite set.

Permutations et partitions : tableaux à marges égales et distance partitionnelle

Permuting the partitions of a prime

Plane Partitions (III): The Weak MacDonald Conjecture.

Plane partitions IV: A conjecture of Mills-Robbins-Rumsey.

Polynomial identities which imply identities of Euler and Jacobi

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