For a given n, what is the smallest number k such that every sequence of length n is determined by the multiset of all its k-subsequences? This is called the k-deck problem for sequence reconstruction, and has been generalized to the two-...

We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m ∈ [ 0 , 2 n ] of the n-dimensional binary affine space AG ( n , 2 ). Following the theme of Erdős, Füredi, Rothschild and T. Sós, we partially ...

We investigate locally n × n grid graphs, that is, graphs in which the neighbourhood of any vertex is the Cartesian product of two complete graphs on n vertices. We consider the subclass of these graphs for which each pair of vertices at distance ...

The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau T, a 1-minor of T is a tableau obtained by first deleting any cell of T, and then performing jeu de taquin slides to fill the ...

We construct an infinite family of hyperovals on the Klein quadric Q + ( 5 , q ), q even. The construction makes use of ovoids of the symplectic generalized quadrangle W ( q ) that is associated with an elliptic quadric which arises as solid ...

Ferrers diagram rank-metric codes were introduced by Etzion and Silberstein in 2009. In their work, they proposed a conjecture on the largest dimension of a space of matrices over a finite field whose nonzero elements are supported on a given ...

Cluster exchange groupoids are introduced by King-Qiu as an enhancement of cluster exchange graphs to study stability conditions and quadratic differentials. In this paper, we introduce the cluster exchange groupoid for any finite Coxeter-Dynkin ...

In this paper, we present a study on polyominoes, which are polygons created by connecting unit squares along their edges. Specifically, we focus on a related concept called a bargraph, which is a path on a lattice in Z ≥ 0 × Z ≥ 0 traced along ...

In this paper, we refine a result of Andrews and Merca on truncated pentagonal number series. Subsequently, we establish some positivity results involving Andrews–Gordon–Bressoud identities and d-regular partitions. In particular, we prove ...

In this note we show that a flag-transitive automorphism group G of a non-trivial 2-( v , k , λ ) design with λ ≥ ( r , λ ) 2 is not of product action type. In conclusion, G is a primitive group of affine or almost simple type.

In this paper, we introduce new interpretations for the sum of the parts with the same parity in all the partitions of n.

We determine asymptotic growth rates for lengths of monochromatic arithmetic progressions in certain automatic sequences. In particular, we look at (one-sided) fixed points of aperiodic, primitive, bijective substitutions and spin substitutions, ...

We give a combinatorial proof of Stanley's shuffle theorem by using the insertion lemma of Haglund, Loehr and Remmel. Based on this combinatorial construction, we establish several refinements of Stanley's shuffle theorem.

A family F of sets is union-closed if the union of any two sets from F belongs to F. The union-closed sets conjecture states that if F is a finite union-closed family of finite sets, then there is an element that belongs to at least half of the ...

The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e. when the goal is to decide if two common independent sets suffice or not. ...

A vertex triple ( u , v , w ) of a graph is called a 2-geodesic if v is adjacent to both u and w and u is not adjacent to w. A graph is said to be 2-geodesic transitive if its automorphism group is transitive on the set of 2-geodesics. In this ...

We prove a new Elekes-Szabó type estimate on the size of the intersection of a Cartesian product A × B × C with an algebraic surface { f = 0 } over the reals. In particular, if A , B , C are sets of N real numbers and f is a trivariate polynomial,...

We show that the maximum cardinality of an equiangular line system in R 18 is at most 59. Our proof includes a novel application of the Jacobi identity for complementary subgraphs. In particular, we show that there does not exist a graph whose ...

Triangulations of a product of two simplices and, more generally, of root polytopes are closely related to Gelfand-Kapranov-Zelevinsky's theory of discriminants, to tropical geometry, tropical oriented matroids, and to generalized permutohedra. ...

This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. A pattern is avoidable if there exist ...