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Results tagged with co.combinatorics
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user 490128
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
1
vote
Accepted
Number of distinct entries in a rotation invariant cube
Since rotations give only even permutations, the 3 distinct index triples $\{a,b,c\}$ with $a \neq b \neq c \neq a$ give twice as much distinct entries as you gave: entries at $(a,b,c)$ and $(b,a,c)$ …
- 1,245
5
votes
About the Hadamard conjecture
Using the Paley construction I, we obtain Hadamard matrices of size $4, 8, 12, 20, 24, 28, 32, 44, 48, 60, 68, 72, 80, 84, 88$. Using Paley Construction II we add $36=2(17+1)$, $52=2(25+1)$, $76=2(37+ …
- 1,245
3
votes
Accepted
On the half-skew-centrosymmetric Hadamard matrices
Let $H_n$ be an $n×n$ Hadamard matrix and $R_n$ the $n×n$ reverse identity matrix.
The matrix $X= \begin{pmatrix}
H_n & R_nH_n \\
H_n & -R_nH_n
\end{pmatrix}$ has entries of length $1$ and $$XX^* = 2n …
- 1,245