Related papers: A new Boolean matrix representation for Catalan se…
We use computer algebra to study the 512-dimensional associative algebra Q B_3, the rational monoid algebra of 3 x 3 Boolean matrices. We obtain a basis for the radical in bijection with the 42 non-regular elements of B_3. The center of the…
In this paper we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of $M_{n}$, $GL_{n}$ and $SL_{n}$ are the centralizers of the trace $x_{1,1}+\dots+x_{n,n}$ in each algebra, for…
For the ideal $I = \langle y_1 + \dots + y_n, y^2_1, \dots , y^2_n \rangle$ in $R = {\mathbb F}[y_1, \dots , y_n]$ with char($\mathbb F$) = 0, we show that the reduced Gr\"obner basis with lex-order consists of polynomials $g_\alpha$ that…
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
We extend, in significant ways, the theory of truncated boolean representable simplicial complexes introduced in 2015. This theory, which includes all matroids, represents the largest class of finite simplicial complexes for which…
We use the concept of the half of a lower-triangular matrix to define a transformation on integer sequences. We explore the properties of this transformation, including in some cases a study of the Hankel transform of the transformed…
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…
The exponential of an NxN matrix can always be expressed as a matrix polynomial of order N-1. In particular, a general group element for the fundamental representation of SU(N) can be expressed as a matrix polynomial of order N-1 in a…
We extend Grood's tableau construction of irreducible representations of the rook monoid and Steinberg's analogous result for the full transformation monoid. Our approach is characteristic-free and applies to any submonoid $\mathcal{M}(n)$…
This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of…
We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles…
It is shown that max-preserving maps (or join-morphisms) on the positive orthant in Euclidean $n$-space endowed with the component-wise partial order give rise to a semiring. This semiring admits a closure operation for maps that generate…
We establish a novel connection between the central binomial coefficients $\binom{2n}{n}$ and Gould's sequence through the construction of a specialized multivariate polynomial quotient ring. Our ring structure is characterized by ideals…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
Exponential Puiseux semirings are additive submonoids of $\qq_{\geq 0}$ generated by almost all of the nonnegative powers of a positive rational number, and they are natural generalizations of rational cyclic semirings. In this paper, we…
We describe an inner product on the diagrams on which the Temperley-Lieb algebra can be represented. We exhibit several constructions which are in natural combinatorial bijection with these diagrams, which are generalizations of various…
For integers m, n $\ge$ 1, we describe a bijection sending dissections of the (mn + 2)-regular polygon into (m + 2)-sided polygons to a new basis of the quotient of the polynomial algebra in mn variables by an ideal generated by some kind…