Zobrazeno 1 - 10
of 294
pro vyhledávání: '"Fallat, Shaun"'
A $n$-by-$n$ matrix is called totally positive ($TP$) if all its minors are positive and $TP_k$ if all of its $k$-by-$k$ submatrices are $TP$. For an arbitrary totally positive matrix or $TP_k$ matrix, we investigate if the $r$th compound ($1
Externí odkaz:
http://arxiv.org/abs/2405.06069
Autor:
Fallat, Shaun, Mojallal, Seyed Ahmad
In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-cli
Externí odkaz:
http://arxiv.org/abs/2307.09663
We investigate the sparsity of null vectors of real symmetric matrices whose off-diagonal pattern of zero and nonzero entries is described by the adjacencies of a graph. We use the definition of the spark of a matrix, the smallest number of nonzero c
Externí odkaz:
http://arxiv.org/abs/2307.00376
A hypertree is a connected hypergraph without cycles. Further a hypertree is called an $r$-tree if, additionally, it is $r$-uniform. Note that 2-trees are just ordinary trees. A classical result states that for any 2-tree $T$ with characteristic poly
Externí odkaz:
http://arxiv.org/abs/2306.16247
Autor:
Fallat, Shaun, Joshi, Neha, Maleki, Roghayeh, Meagher, Karen, Mojallal, Seyed Ahmad, Nasserasr, Shahla, Shirazi, Mahsa N., Razafimahatratra, Andriaherimanana Sarobidy, Stevens, Brett
Zero forcing is a combinatorial game played on a graph with the ultimate goal of changing the colour of all the vertices at minimal cost. Originally this game was conceived as a one player game, but later a two-player version was devised in-conjuncti
Externí odkaz:
http://arxiv.org/abs/2306.01138
Publikováno v:
Linear Algebra Appl. 694, 2024, pages 360-413
A real linear combination of products of minors which is nonnegative over all totally nonnegative (TN) matrices is called a determinantal inequality for these matrices. It is referred to as multiplicative when it compares two collections of products
Externí odkaz:
http://arxiv.org/abs/2305.16485
Autor:
Barrett, Wayne, Fallat, Shaun, Furst, Veronika, Nasserasr, Shahla, Rooney, Brendan, Tait, Michael
For an $n \times n$ matrix $A$, let $q(A)$ be the number of distinct eigenvalues of $A$. If $G$ is a connected graph on $n$ vertices, let $\mathcal{S}(G)$ be the set of all real symmetric $n \times n$ matrices $A=[a_{ij}]$ such that for $i\neq j$, $a
Externí odkaz:
http://arxiv.org/abs/2305.10562
Autor:
Allred, Sarah, Curl, Emelie, Fallat, Shaun, Nasserasr, Shahla, Schuerger, Houston, Villagrán, Ralihe R., Vishwakarma, Prateek K.
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently the class of graphs in which all associated symmetric matrices possess
Externí odkaz:
http://arxiv.org/abs/2303.17138
Autor:
Abiad, Aida, Fallat, Shaun M., Kempton, Mark, Levene, Rupert H., Oblak, Polona, Šmigoc, Helena, Tait, Michael, Meulen, Kevin Vander
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on bordering a mat
Externí odkaz:
http://arxiv.org/abs/2303.07949