A conjecture on permanents

AbstractWe show, by a direct proof, that the n × n (0, 1) matrix with the last n − 1 entries on the main diagonal equal to 0 and all the other entries equal to 1 is never barycentric for n ≥ 4, which was a conjecture of R. A. Brualdi on permanents

Commutative Energetic Subsets of BCK-Algebras

The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal

A characterization of linear operators that preserve isolation numbers

We obtain characterizations of Boolean linear operators that preserve some of the isolation numbers of Boolean matrices. In particular, we show that the following are equivalent: (1) $T$ preserves the isolation number of all matrices; (2) $T$ preserves the set of matrices with isolation number one and the set of those with isolation number $k$ for some $2leq kleq min{m,n}$; (3) for $1leq kleq min{m,n}-1$, $T$ preserves matrices with isolation number $k$, and those with isolation number $k+1$, (4) $T$ maps $J$ to $J$ and preserves the set of matrices of isolation number 2; (5) $T$ is a $(P,Q)$-operator, that is, for fixed permutation matrices $P$ and $Q$, $mtimes n$ matrix $X,$~ $T(X)=PXQ$ or, $m=n$ and $T(X)=PX^tQ$ where $X^t$ is the transpose of $X$

Neutrosophic Commutative N-Ideals in BCK-Algebras

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered

Group signatures in practice

10 páginas, 2 figuras, 1 tabla. International Joint Conference. CISIS’15 and ICEUTE’15Group signature schemes allow a user to sign a message in an anonymous way on behalf of a group. In general, these schemes need the collaboration of a Key Generation Center or a Trusted Third Party, which can disclose the identity of the actual signer if necessary (for exam- ple, in order to settle a dispute). This paper presents the results obtained after implementing a group signature scheme using the Integer Factoriza- tion Problem and the Subgroup Discrete Logarithm Problem, which has allowed us to check the feasibility of the scheme when using big numbers.This work has been partially supported under the framework of the international cooperation program managed by National Research Foundation of Korea (NRF- 2013K2A1A2053670) and by Comunidad de Madrid (Spain) under the project S2013/ICE-3095-CM (CIBERDINE).Peer reviewe

Linear operators that strongly preserve regularity of fuzzy matrices

An $ntimes n$ fuzzy matrix $A$ is called {regular} if there is an $ntimes n$ fuzzy matrix $G$ such that $AGA=A$. We study the problem of characterizing those linear operators $T$ on the fuzzy matrices such that $T(X)$ is regular if and only if $X$ is. Consequently, we obtain that $T$ strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices $P$ and $Q$ such that it has the form $T(X)=PXQ$ or $T(X)=PX^tQ$ for all fuzzy matrices $X$

Linear Operators That Preserve Two Genera of a Graph

If a graph can be embedded in a smooth orientable surface of genus g without edge crossings and can not be embedded on one of genus g − 1 without edge crossings, then we say that the graph has genus g. We consider a mapping on the set of graphs with m vertices into itself. The mapping is called a linear operator if it preserves a union of graphs and it also preserves the empty graph. On the set of graphs with m vertices, we consider and investigate those linear operators which map graphs of genus g to graphs of genus g and graphs of genus g + j to graphs of genus g + j for j ≤ g and m sufficiently large. We show that such linear operators are necessarily vertex permutations

Linear preservers of term ranks of matrices over semirings

AbstractThe term rank of a matrix A over a semiring S is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we study linear operators that preserve term ranks of matrices over S. In particular, we show that a linear operator T on matrix space over S preserves term rank if and only if T preserves term ranks 1 and α(≥2) if and only if T preserves two consecutive term ranks in a restricted condition. Other characterizations of term-rank preservers are also given

Rook polynomials to and from permanents

AbstractIn this paper, we find an expression of the rook vector of a matrix A (not necessarily square) in terms of permanents of some matrices associated with A, and obtain some simple exact formulas for the permanents of all n×n Toeplitz band matrices of zeros and ones whose bands are of width not less than n−1

Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established