Richard A. Brualdi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Richard A. Brualdi has a total of 58 co-authors. Here are the top co-authors by number of shared publications:
- Geir Dahl
Department of Mathematics, University of Oslo, Oslo, Norway
10 shared publications - Kathleen P. Kiernan
Department of Mathematics University of Wisconsin Madison 53706 WI
7 shared publications - Lei Cao
Department of Mathematics Halmos College Nova Southeastern University Fort Lauderdale FL USA
6 shared publications - Seth A. Meyer
Department of Mathematics University of Wisconsin Madison 53706 WI
5 shared publications Eliseu Fritscher
University of Wisconsin
4 shared publications- Michael W. Schroeder
Department of Mathematics University of Wisconsin Madison 53706 WI
4 shared publications
Latest Publications
- 6 January 2025
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 41 (1) , 1-21
$12\cdots t$-Permutation Avoiding (0, 1)-Matrices- 6 January 2025
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 41 (1) , 1-21
$12\cdots t$-Permutation Avoiding (0, 1)-Matrices- Open Access
- 7 February 2024
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 40 (2) , 1-22
Multipermutations and Stirling Multipermutations
We consider multipermutations and a certain partial order, the weak Bruhat order, on this set. This generalizes the Bruhat order for permutations, and is defined in terms of containment of inversions. Different characterizations of this order are given. We also study special multipermutations called Stirling multipermutations and their properties.
- 7 February 2024
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 40 (2) , 1-22
Open AccessMultipermutations and Stirling Multipermutations
We consider multipermutations and a certain partial order, the weak Bruhat order, on this set. This generalizes the Bruhat order for permutations, and is defined in terms of containment of inversions. Different characterizations of this order are given. We also study special multipermutations called Stirling multipermutations and their properties.
- 24 July 2023
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 697, 49-81
123-avoiding doubly stochastic matrices
- 24 July 2023
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 697, 49-81
123-avoiding doubly stochastic matrices
- Open Access
- 18 May 2023
- Published by University of Wyoming Libraries in The Electronic Journal of Linear Algebra
- Vol. 39, 260-281
Multi-alternating sign matrices
We introduce a generalization of alternating sign matrices (ASMs) called multiASMs and develop some of their properties. Classes of multiASMs with specified row and column sum vectors $R$ and $S$ extend the classes of $(0,1)$-matrices with specified $R$ and $S$. The special case when $R=S$ is a constant vector, in particular all 2's, is treated in more detail. We also investigate the polytope spanned by a class of multiASMs. Finally, we discuss the possibility of defining a Bruhat order on a class of multiASMs.- 18 May 2023
- Published by University of Wyoming Libraries in The Electronic Journal of Linear Algebra
- Vol. 39, 260-281
Open AccessMulti-alternating sign matrices
We introduce a generalization of alternating sign matrices (ASMs) called multiASMs and develop some of their properties. Classes of multiASMs with specified row and column sum vectors $R$ and $S$ extend the classes of $(0,1)$-matrices with specified $R$ and $S$. The special case when $R=S$ is a constant vector, in particular all 2's, is treated in more detail. We also investigate the polytope spanned by a class of multiASMs. Finally, we discuss the possibility of defining a Bruhat order on a class of multiASMs. - Open Access
- 12 January 2023
- Published by University of Primorska Press in The Art of Discrete and Applied Mathematics
Permutation graphs and the weak Bruhat order
Permutation graphs are graphs associated with permutations where edges represent inversions. We study different classes of permutation graphs and isomorphic permutation graphs. A complete answer of a basic isomorphism question is given for trees. A connection to the majorization order for integer partitions is established, in connection with the notion of inversion vectors. Finally, we study special transitivity properties related to inversions of permutations.
- 12 January 2023
- Published by University of Primorska Press in The Art of Discrete and Applied Mathematics
Open AccessPermutation graphs and the weak Bruhat order
Permutation graphs are graphs associated with permutations where edges represent inversions. We study different classes of permutation graphs and isomorphic permutation graphs. A complete answer of a basic isomorphism question is given for trees. A connection to the majorization order for integer partitions is established, in connection with the notion of inversion vectors. Finally, we study special transitivity properties related to inversions of permutations.
- 25 September 2021
- Published by University of Wyoming Libraries in The Electronic Journal of Linear Algebra
- Vol. 37, 613-639
Alternating sign and sign-restricted matrices: representations and partial orders
Sign-restricted matrices (SRMs) are $(0, \pm 1)$-matrices where, ignoring 0's, the signs in each column alternate beginning with a $+1$ and all partial row sums are nonnegative. The most investigated of these matrices are the alternating sign matrices (ASMs), where the rows also have the alternating sign property, and all row and column sums equal 1. We introduce monotone triangles to represent SRMs and investigate some of their properties and connections to certain polytopes. We also investigate two partial orders for ASMs related to their patterns alternating cycles and show a number of combinatorial properties of these orders.- 25 September 2021
- Published by University of Wyoming Libraries in The Electronic Journal of Linear Algebra
- Vol. 37, 613-639
Alternating sign and sign-restricted matrices: representations and partial orders
Sign-restricted matrices (SRMs) are $(0, \pm 1)$-matrices where, ignoring 0's, the signs in each column alternate beginning with a $+1$ and all partial row sums are nonnegative. The most investigated of these matrices are the alternating sign matrices (ASMs), where the rows also have the alternating sign property, and all row and column sums equal 1. We introduce monotone triangles to represent SRMs and investigate some of their properties and connections to certain polytopes. We also investigate two partial orders for ASMs related to their patterns alternating cycles and show a number of combinatorial properties of these orders.- 4 August 2021
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 304, 196-211
Pattern-avoiding -matrices and bases of permutation matrices- 4 August 2021
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 304, 196-211
Pattern-avoiding -matrices and bases of permutation matrices- Open Access
- 1 July 2021
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 297, 21-34
Convex -matrices and their epitopes- 1 July 2021
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 297, 21-34
Open AccessConvex -matrices and their epitopes - 1 January 2021
- Published by ISTE Group in Advances in Pure and Applied Mathematics
- Vol. 12 (Special) , 1-14
Permutation (Matrices) and Beyond
This is an exposition of my keynote talk given at The Third International Conference on Mathematics and Statistics: AUS-ICMS February 2020, Sharjah, UAE. It concerns permutations and permutation (...)
- 1 January 2021
- Published by ISTE Group in Advances in Pure and Applied Mathematics
- Vol. 12 (Special) , 1-14
Permutation (Matrices) and Beyond
This is an exposition of my keynote talk given at The Third International Conference on Mathematics and Statistics: AUS-ICMS February 2020, Sharjah, UAE. It concerns permutations and permutation (...)
- 22 November 2020
- Published by Springer Nature
- p. 109-152
Hankel Tournaments and Special Oriented Graphs
- 22 November 2020
- Published by Springer Nature
- p. 109-152
Hankel Tournaments and Special Oriented Graphs