Plethysm for wreath products and homology of sub-posets of Dowling lattices.

Henderson, Anthony

Displaying similar documents to “Plethysm for wreath products and homology of sub-posets of Dowling lattices.”

The number of representations by sums of squares and triangular numbers.

Lam, Heung Yeung (2007)

Integers

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On the mean value of a sum analogous to character sums over short intervals

Ren Ganglian, Zhang Wenpeng (2008)

Czechoslovak Mathematical Journal

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The main purpose of this paper is to study the mean value properties of a sum analogous to character sums over short intervals by using the mean value theorems for the Dirichlet L-functions, and to give some interesting asymptotic formulae.

A generalization of a result of Fermat.

Gica, Alexandru (2007)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Divisibility by 2 and 3 of certain Stirling numbers.

Davis, Donald M. (2008)

Integers

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BG-ranks and 2-cores.

Chen, William Y.C., Ji, Kathy Q., Wilf, Herbert S. (2006)

The Electronic Journal of Combinatorics [electronic only]

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Bijective proofs of parity theorems for partition statistics.

Shattuck, Mark (2005)

Journal of Integer Sequences [electronic only]

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On the equation $m - 1 = a ϕ (m)$ .

Deaconescu , Marian (2006)

Integers

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On a partition function of Richard Stanly.

Andrews, George E. (2004)

The Electronic Journal of Combinatorics [electronic only]

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Congruences for certain binomial sums

Jung-Jo Lee (2013)

Czechoslovak Mathematical Journal

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We exploit the properties of Legendre polynomials defined by the contour integral $𝐏_{n} (z) = {(2 π i)}^{- 1} \oint {(1 - 2 t z + t^{2})}^{- 1 / 2} t^{- n - 1} d t,$ where the contour encloses the origin and is traversed in the counterclockwise direction, to obtain congruences of certain sums of central binomial coefficients. More explicitly, by comparing various expressions of the values of Legendre polynomials, it can be proved that for any positive integer $r$ , a prime $p ⩾ 5$ and $n = r p^{2} - 1$ , we have $\sum_{k = 0}^{⌊ n / 2 ⌋} (\binom{2 k}{k}) \equiv 0, 1 or - 1 (mod p^{2})$ , depending on the value of $r (mod 6)$ .

Properties of G-atoms and full Galois covering reduction to stabilizers

Piotr Dowbor (2000)

Colloquium Mathematicae

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Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra $E n d_{R} (B)$ of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective $E n d_{R} (B)$ -module ${(E n d_{R} (B))}^{*}$ is indecomposable (Corollary 3.1) and the socle of the tensor product functor $- \otimes_{R} B^{*}$ is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors $Φ^{U} : ∐_{B \in U} m o d k G_{B} \to m o d (R / G)$ and $Ψ^{U} : m o d (R / G) \to \prod_{B \in U} m o d k G_{B}$ )is full (resp. strictly full)...