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$(0, 1)$ -matrices, discrepancy and preservers

LeRoy B. Beasley (2019)

Czechoslovak Mathematical Journal

Let $m$ and $n$ be positive integers, and let $R = (r_{1}, ..., r_{m})$ and $S = (s_{1}, ..., s_{n})$ be nonnegative integral vectors. Let $A (R, S)$ be the set of all $m \times n$ $(0, 1)$ -matrices with row sum vector $R$ and column vector...

$(- 1)$ -enumeration of self-complementary plane partitions.

Eisenkölbl, Theresia (2005)

The Electronic Journal of Combinatorics [electronic only]

$2 - (n^{2}, 2 n, 2 n - 1)$ designs obtained from affine planes

Andrea Caggegi (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The simple incidence structure $𝒟 (𝒜, 2)$ formed by points and unordered pairs of distinct parallel lines of a finite affine plane $𝒜 = (𝒫, ℒ)$ of order $n > 2$ is a $2 - (n^{2}, 2 n, 2 n - 1)$ design. If $n = 3$ , $𝒟 (𝒜, 2)$ is the complementary design of $𝒜$ . If $n = 4$ , $𝒟 (𝒜, 2)$ is isomorphic to the geometric design $A G_{3} (4, 2)$ (see [2; Theorem 1.2]). In this paper we give necessary and sufficient conditions for a $2 - (n^{2}, 2 n, 2 n - 1)$ design to be of the form $𝒟 (𝒜, 2)$ for some finite affine plane $𝒜$ of order $n > 4$ . As a consequence we obtain a characterization of small designs $𝒟 (𝒜, 2)$ .

There is described a procedure which determines the quasigroup identity corresponding to a given 3-coloured 3-configuration with a simple edge basis.

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Displaying 1 – 20 of 46

$(0, 1)$ -matrices, discrepancy and preservers

$(- 1)$ -enumeration of self-complementary plane partitions.

$2 - (n^{2}, 2 n, 2 n - 1)$ designs obtained from affine planes

24 self-inscribed decagons in Desargues configuration $10_{3}$

2-adic behavior of numbers of domino tilings.

$3$ -configurations with simple edge basis and their corresponding quasigroup identities

3-designs from PGL $(2, q)$ .

5-sparse Steiner triple systems of order $n$ exist for almost all admissible $n$ .

...-Morphic Sets of Prototiles.

(rn-1, r) Hjelmslev-Ebenen des Typs n.

"What Is a Complex Matroid?"

$Δ$ -matroid and jump system.

$Δ$ -matroids and Pfaffian forms.

Аутоморфизмы одного класса конфигураций

Допустимые n- арные квазигруппы. II

Допустимые n-квазигруппы. Связь допустимости с ортогональностью

Зеркальные конфигурации точек и прямых и алгебраические поверхности степени 4

Исправления к статье "Некоторые замечания о дискретной хроногеометрии". (См. журнал 1978, т.19, N 1, с.186-192).

Квазипериодические покрытия и квазикристаллы

Комбинаторные схемы и алгебры

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