AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we show that if for every distinct elements x,y∈S, x+y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring
AbstractLet f(k) be the largest number such that each k-regular bipartite graph with 2n vertices has...
AbstractWe show that for any subset E⊆Fqd with |E|≫qd−1+2d, the number of singular matrices whose ro...
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the i...
AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we s...
AbstractLet R be a ring and X⊆R be a non-empty set. The regular graph of X, Γ(X), is defined to be t...
AbstractLet R be a ring and X⊆R be a non-empty set. The regular graph of X, Γ(X), is defined to be t...
We give a generating function for the number of pairs of $n\times n$ matrices $(A, B)$ over a finite...
The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the verte...
AbstractLet R be a non-commutative ring and Z(R) be its center. The commuting graph of R is defined ...
AbstractLet Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of ele...
AbstractFor a positive integer r we consider the set Br of all values of kn for which there exists a...
AbstractWe will prove that generalized clique polynomials of vertex-weighted simple graphs coincide ...
AbstractLet R be a ring (not necessarily commutative) with 1. Following Sharma and Bhatwadekar [P.K....
A $0,1$ matrix is said to be regular if all of its rows and columns have the same number of ones. We...
AbstractLet F be a field and let G be a finite graph with a total ordering on its edge set. Richard ...
AbstractLet f(k) be the largest number such that each k-regular bipartite graph with 2n vertices has...
AbstractWe show that for any subset E⊆Fqd with |E|≫qd−1+2d, the number of singular matrices whose ro...
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the i...
AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we s...
AbstractLet R be a ring and X⊆R be a non-empty set. The regular graph of X, Γ(X), is defined to be t...
AbstractLet R be a ring and X⊆R be a non-empty set. The regular graph of X, Γ(X), is defined to be t...
We give a generating function for the number of pairs of $n\times n$ matrices $(A, B)$ over a finite...
The annihilator graph $AG(R)$ of a commutative ring $R$ is a simple undirected graph with the verte...
AbstractLet R be a non-commutative ring and Z(R) be its center. The commuting graph of R is defined ...
AbstractLet Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of ele...
AbstractFor a positive integer r we consider the set Br of all values of kn for which there exists a...
AbstractWe will prove that generalized clique polynomials of vertex-weighted simple graphs coincide ...
AbstractLet R be a ring (not necessarily commutative) with 1. Following Sharma and Bhatwadekar [P.K....
A $0,1$ matrix is said to be regular if all of its rows and columns have the same number of ones. We...
AbstractLet F be a field and let G be a finite graph with a total ordering on its edge set. Richard ...
AbstractLet f(k) be the largest number such that each k-regular bipartite graph with 2n vertices has...
AbstractWe show that for any subset E⊆Fqd with |E|≫qd−1+2d, the number of singular matrices whose ro...
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the i...
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