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This article considers the eta power $\prod_{(1 - q^{k})}^{b - 1}$ . It is proved that the coefficients of $q^{n} / n!$ in this expression, as polynomials in b, exhibit equidistribution of the coefficients in the nonzero residue classes mod 5 when n = 5j+4. Other symmetries, as well as symmetries for other primes and prime powers, are proved, and some open questions are raised.

Polynomial extension of Fleck's congruence

Zhi-Wei Sun (2006)

Acta Arithmetica

Polynomials of multipartitional type and inverse relations

Miloud Mihoubi, Hacène Belbachir (2011)

Discussiones Mathematicae - General Algebra and Applications

Chou, Hsu and Shiue gave some applications of Faà di Bruno's formula to characterize inverse relations. Our aim is to develop some inverse relations connected to the multipartitional type polynomials involving to binomial type sequences.

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p-adic valuations of some sums of multinomial coefficients

Parity theorems for statistics on lattice paths and Laguerre configurations.

Partial Bell polynomials and inverse relations.

Pascal's triangle (mod 9)

Permutations avoiding an increasing number of length-increasing forbidden subsequences.

Pilesize dynamic one-pile Nim and Beatty's theorem.

Playing with some identities of Andrews.

Polynomial analogues of Ramanujan congruences for Han's hooklength formula

Polynomial extension of Fleck's congruence

Polynomials of multipartitional type and inverse relations

Powers of a matrix and combinatorial identities.

Prime divisors of $q$ -binomial coefficients

Prime factors of binomial coefficients and related problems

Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten.

Properties of the van der Pol numbers and polynomials.

Propriétés arithmétiques des polynômes d'Euler

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