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We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $| q_{0} | = ... = | q_{N - 1} | = 1$ the quantity $Φ = \sum_{i + k = j + l} \frac{q_{i} q_{k}}{q_{j} q_{l}}$ satisfies $Φ \geq N^{2}$ , with equality if and only if $q = (q_{i})$ is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of $Φ$ , (2) the study of the critical points of $Φ$ , and (3) the computation of the moments of $Φ$ . We explore here these questions,...

Another case of the prime power conjecture for finite projective planes.

Jungnickel, Dieter, de Resmini, Marialuisa J. (2002)

Advances in Geometry

Another product construction for large sets of resolvable directed triple systems.

Zhao, Hongtao (2009)

The Electronic Journal of Combinatorics [electronic only]

Answer to one of Fishburn's questions: ``Isosceles planar subsets'' [Discrete Comput. Geom. 19 (1998), no. 3, 391--398]

Vojtech Bálint, Zuzana Kojdjaková (2001)

Archivum Mathematicum

Our short note gives the affirmative answer to one of Fishburn’s questions.

Antiflexible Latin directed triple systems

Andrew R. Kozlik (2015)

Commentationes Mathematicae Universitatis Carolinae

It is well known that given a Steiner triple system one can define a quasigroup operation $\cdot$ upon its base set by assigning $x \cdot x = x$ for all $x$ and $x \cdot y = z$ , where $z$ is the third point in the block containing the pair ${x, y}$ . The same can be done for Mendelsohn triple systems, where $(x, y)$ is considered to be ordered. But this is not necessarily the case for directed triple systems. However there do exist directed triple systems, which induce a quasigroup under this operation and these are called Latin directed triple systems....

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An extension of matroid rank submodularity and the $Z$ -Rayleigh property.

An extremal characterization of projective planes.

An Infinite Family of Minor-Minimal Nonrealizable 3-Chirotopes.

An infinite family of non-embeddable Hadamard designs.

An inversion formula, matrix functions, combinatorial identities and graphs

An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits.

Analysis of PBIB Designs Using Association Matrices.

Analytic aspects of the circulant Hadamard conjecture

Another case of the prime power conjecture for finite projective planes.

Another product construction for large sets of resolvable directed triple systems.

Answer to one of Fishburn's questions: ``Isosceles planar subsets'' [Discrete Comput. Geom. 19 (1998), no. 3, 391--398]

Antiflexible Latin directed triple systems

Aperiodic Tiles.

Applications of combinatorics to statics – a survey

Applying balanced generalized weighing matrices to construct block designs.

Arcs with large conical subsets.

Arrangements of Lines with a Minimum Number of Triangles Are Simple.

Arranging numbers on circles to reach maximum total variations.

Association schemes. I

Association schemes. II

Currently displaying 121 – 140 of 1135