Yaroslav N. Shitov

activity

20102020

most citedHow hard is the tensor rank?

21 citations · 41 across the 14 of their papers we have counts for

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26 papers · 1 filter

math.CO2020

A sign pattern with non-zero elements on the diagonal whose minimal rank realizations are not diagonalizable over the complex numbers

Yaroslav Shitov

The rank of the $9 \times 9$ matrix $$ \left( \begin{array}{cccc|c|cccc} 1&1&0&0&1&0&0&0&0\\ 1&1&0&0&0&0&0&0&0\\ 0&0&1&1&1&0&0&0&0\\ 0&0&1&1&0&0&0&0&0\\\hline 0&0&0&0&1&0&1&0&1\\\hl…

math.CO2019

Linear mappings preserving the copositive cone

Yaroslav Shitov

Let $S_{n}$ be the set of all $n$ -by- $n$ symmetric real matrices, and let $C_{n}$ be the copositive cone, that is, the set of all matrices $a \in S_{n}$ that…

math.CO2019

Counterexamples to Hedetniemi's conjecture

Yaroslav Shitov

The chromatic number of $G \times H$ can be smaller than the minimum of the chromatic numbers of finite simple graphs $G$ and $H$ .

math.CO2019★ 1 cited

The ring $M_{8 k + 4} (Z_{2})$ is nil-clean of index four

Yaroslav Shitov

We show that the direct sum of an odd number of matrices $C = 0100001000011001$ cannot be a sum $P + Q$ of matrices…

math.CO2019

One more counterexample on sign patterns

Yaroslav Shitov

The \textit{sepr-sequence} of an $n \times n$ real matrix $A$ is $(s_{1}, \dots, s_{n})$ , where $s_{k}$ is the subset of those signs of $+, -, 0$ that appear in the values of the $k \times k$ …

math.CO2019

An improvement to a recent upper bound for synchronizing words of finite automata

Yaroslav Shitov

It has been known since the 60's that any complete discrete $n$ -state automaton admits a reset word of length not exceeding $α n^{3} + o (n^{3})$ for some absolute constant $α$ . J.-E. Pin…

A sign pattern with non-zero elements on the diagonal whose minimal rank realizations are not diagonalizable over the complex numbers

Linear mappings preserving the copositive cone

Counterexamples to Hedetniemi's conjecture

The ring M8k+4​(Z2​) is nil-clean of index four

One more counterexample on sign patterns

An improvement to a recent upper bound for synchronizing words of finite automata

The ring $M_{8 k + 4} (Z_{2})$ is nil-clean of index four