Related papers: Size-minimal combinatorial designs of staircase ty…
A Metis design is one for which v=r+k+1. This paper deals with Metis designs that are quasi-residual. The parameters of such designs and the corresponding symmetric designs can be expressed by Fibonacci numbers. Although the question of…
In an $n \times n$ array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than $\beta n$ times, the array contains a transversal of…
In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete…
We enumerate smooth and rationally smooth Schubert varieties in the classical finite types A, B, C, and D, extending Haiman's enumeration for type A. To do this enumeration, we introduce a notion of staircase diagrams on a graph. These…
The aim of this paper is to present a construction of $t$-divisible designs for $t>3$, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This…
We computationally completely enumerate a number of types of row-column designs up to isotopism, including double, sesqui and triple arrays as known from the literature, and two newly introduced types that we call mono arrays and AO-arrays.…
Let $R$ and $S$ be two sequences of nonnegative integers in nonincreasing order and with the same sum, and let ${\cal A}(R,S)$ be the class of all $(0,1)$-matrices having row sum $R$ and column sum $S$. For a positive integer $t$, the…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
In this note we focus on combinatorial aspects of plus-one generated line arrangements. We provide combinatorial constraints on such arrangements and we construct a polynomial that decodes the plus-one generated property. We present new…
Let $S$ be an orthogonal array $OA(d,k)$ and let $c$ be an $r$--coloring of its ground set $X$. We give a combinatorial identity which relates the number of vectors in $S$ with given color patterns under $c$ with the cardinalities of the…
The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A classical result of Gantmacher-Krein assures the existence of SSR…
An $r$-matrix is a matrix with symbols in $\{0,1,\dots,r-1\}$. A matrix is simple if it has no repeated columns. Let the support of a matrix $F$, $\text{supp}(F)$ be the largest simple matrix such that every column in $\text{supp}(F)$ is in…
We use the 0-1 tableaux as a tool for enumerating permutations and partitions with restricted minima. The method used is extended for permutation pairs and partition pairs generated by a bipartite 0-1 tableaux.
We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\alpha_n}, {n-1}^{\alpha_{n-1}},..., 1^{\alpha_1})$, where $\alpha = (\alpha_1,...,\alpha_n)$ is a composition, or the $180^\circ$ rotation of…
Let $\{p_1,\dots,p_n\}$ and $\{q_1,\dots,q_n\}$ be two sets of $n$ labeled points in general position in the plane. We say that these two point sets have the same order type if for every triple of indices $(i,j,k)$, $p_k$ is above the…
Looking at incidence matrices of $t$-$(v,k,\lambda)$ designs as $v \times b$ matrices with $2$ possible entries, each of which indicates incidences of a $t$-design, we introduce the notion of a $c$-mosaic of designs, having the same number…
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
Given a real symmetric $n\times n$ matrix, the sepr-sequence $t_1\cdots t_n$ records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence…