Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Valyuzhenich, Alexandr"'
In this work, we prove that for every $k\geq 3$ there exist arbitrarily long bicrucial $k$-power-free permutations. We also show that for every $k\geq 3$ there exist right-crucial $k$-power-free permutations of any length at least $(k-1)(2k+1)$.
Externí odkaz:
http://arxiv.org/abs/2409.01206
Autor:
Valyuzhenich, Alexandr
The spectrum of a complex-valued function $f$ on $\mathbb{Z}_{q}^n$ is the set $\{|u|:u\in \mathbb{Z}_q^n~\mathrm{and}~\widehat{f}(u)\neq 0\}$, where $|u|$ is the Hamming weight of $u$ and $\widehat{f}$ is the Fourier transform of $f$. Let $1\leq d'\
Externí odkaz:
http://arxiv.org/abs/2404.10418
Publikováno v:
Discrete Math. 347(10) 2024, 114138(1-14)
A perfect $k$-coloring of the Boolean hypercube $Q_n$ is a function from the set of binary words of length $n$ onto a $k$-set of colors such that for any colors $i$ and $j$ every word of color $i$ has exactly $S(i,j)$ neighbors (at Hamming distance $
Externí odkaz:
http://arxiv.org/abs/2311.05566
Autor:
Valyuzhenich, Alexandr
In this work, we prove a general version of the reduction lemmas for eigenfunctions of graphs admitting involutive automorphisms of a special type.
Externí odkaz:
http://arxiv.org/abs/2305.12849
Autor:
Valyuzhenich, Alexandr
The $n$-dimensional hypercube has $n+1$ distinct eigenvalues $n-2i$, $0\leq i\leq n$, with corresponding eigenspaces $U_i(n)$. In 2021 it was proved by the author that if a function with non-empty support belongs to the direct sum $U_i(n)\oplus U_{i+
Externí odkaz:
http://arxiv.org/abs/2303.10995
Publikováno v:
In Discrete Mathematics October 2024 347(10)
Autor:
Sotnikova, Ev, Valyuzhenich, Alexandr
In this work we present a survey of results on the problem of finding the minimum cardinality of the support of eigenfunctions of graphs.
Comment: 11 fugures
Comment: 11 fugures
Externí odkaz:
http://arxiv.org/abs/2102.11142
Autor:
Valyuzhenich, Alexandr
The Hamming graph $H(n,q)$ is the graph whose vertices are the words of length $n$ over the alphabet $\{0,1,\ldots,q-1\}$, where two vertices are adjacent if they differ in exactly one coordinate. The adjacency matrix of $H(n,q)$ has $n+1$ distinct e
Externí odkaz:
http://arxiv.org/abs/2003.01571
The Star graph $S_n$, $n\ge 3$, is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(12),(13),\ldots,(1n)\}$. In this work we study eigenfunctions of $S_n$ corresponding to the second largest eigenvalue $n-2$.
Externí odkaz:
http://arxiv.org/abs/1910.01374