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pro vyhledávání: '"05B30"'
We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical $(k,k)$-designs and provide certain examples, including unit-norm tight frames, that attain these bounds. The univ
Externí odkaz:
http://arxiv.org/abs/2411.00290
We prove a conjecture of Gy\'arf\'as (1976), which asserts that any family of trees $T_1, \dots, T_{n}$ where each $T_k$ has $k$ vertices packs into $K_n$. We do so by translating the decomposition problem into a labeling problem, namely complete lab
Externí odkaz:
http://arxiv.org/abs/2410.13840
Let $m,n,s,k$ be four integers such that $1\leqslant s \leqslant n$, $1\leqslant k\leqslant m$ and $ms=nk$. A signed magic array $SMA(m,n; s,k)$ is an $m\times n$ partially filled array whose entries belong to the subset $\Omega\subset \mathbb{Z}$, w
Externí odkaz:
http://arxiv.org/abs/2410.04101
Autor:
Roucairol, Milo, Cazenave, Tristan
We are interested in the automatic refutation of spectral graph theory conjectures. Most existing works address this problem either with the exhaustive generation of graphs with a limited size or with deep reinforcement learning. Exhaustive generatio
Externí odkaz:
http://arxiv.org/abs/2409.18626
The relationship between a set of design points and the class of hierarchical polynomial models identifiable from the design is investigated. Saturated models are of particular interest. Necessary and sufficient conditions are derived on the set of d
Externí odkaz:
http://arxiv.org/abs/2409.07062
Autor:
Culus, Jean-François, Toulouse, Sophie
Traditionally, inapproximability results for $\mathsf{Max\,k\,CSP\!-\!q}$ have been established using balanced $t$-wise independent distributions, which are related to orthogonal arrays of strength $t$. We contribute to the field by exploring such co
Externí odkaz:
http://arxiv.org/abs/2409.03903
Autor:
Kong, Xiangliang, Tamo, Itzhak
Incidence problems between geometric objects is a key area of focus in the field of discrete geometry. Among them, the study of incidence problems over finite fields have received a considerable amount of attention in recent years. In this paper, by
Externí odkaz:
http://arxiv.org/abs/2408.10977
Autor:
Jedwab, Jonathan, Pender, Thomas
We give the first general constructions of even length quaternary Legendre pairs: there is a quaternary Legendre pair of length $(q-1)/2$ for every prime power $q$ congruent to $1$ modulo $4$, and there is a quaternary Legendre pair of length $2p$ fo
Externí odkaz:
http://arxiv.org/abs/2408.08472
Autor:
Stömmer, Ralph
Stefan Mandel is the man who won the lottery 14 times. He never disclosed the recipe he called combinatorial condensation, which enabled him to hit the Romanian lottery jackpot in the early phase of his betting career. Combinatorial condensation is f
Externí odkaz:
http://arxiv.org/abs/2408.06857
A $\Gamma$-magic rectangle set $\mathrm{MRS}_\Gamma (a, b; c)$ is a collection of $c$ arrays of size $a\times b$ whose entries are the elements of an abelian group $\Gamma$ of order $abc$, each one appearing once and in a unique array in such a way t
Externí odkaz:
http://arxiv.org/abs/2408.04897