Journal of Combinatorial Theory Series A

In their study of the truncation of Euler's pentagonal number theorem, Andrews and Merca introduced a partition function M k ( n ) to count the number of partitions of n in which k is the least integer that is not a part and there are more parts ...

Let T n be the set of all mappings T : { 1 , 2 , … , n } → { 1 , 2 , … , n }. The corresponding graph of T is a union of disjoint connected unicyclic components. We assume that each T ∈ T n is chosen uniformly at random (i.e., with probability n −...

We study the normal Cayley graphs Cay ( S n , C ( n , I ) ) on the symmetric group S n, where I ⊆ { 2 , 3 , … , n } and C ( n , I ) is the set of all cycles in S n with length in I. We prove that the strictly second largest eigenvalue of Cay ( S ...

We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group S n on the cohomology of Hessenberg varieties extends to generalized Hessenberg varieties and that natural morphisms ...

Group-based models appear in algebraic statistics as mathematical models coming from evolutionary biology, namely in the study of mutations of genomes. Motivated also by applications, we are interested in determining the algebraic degrees of the ...

It is known that Paley graphs of square order have the strict-EKR property, that is, all maximum cliques are canonical cliques. Peisert-type graphs are natural generalizations of Paley graphs and some of them also have the strict-EKR property. ...

Let k , m , n be positive integers with k ⩾ 2. A k-multiset of [ n ] m is a collection of k integers from the set { 1 , 2 , … , n } in which the integers can appear more than once but at most m times. A family of such k-multisets is called an ...

Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently ...

Given a subgroup H of a group ( G , + ), a ( G , H , k , 1 ) difference family (DF) is a set F of k-subsets of G such that { f − f ′ : f , f ′ ∈ F , f ≠ f ′ , F ∈ F } = G ∖ H. Let g Z g h be the subgroup of order h in Z g h generated by g. A ( Z ...

We define the root polytope of a regular oriented matroid, and show that the greedoid polynomial of an Eulerian branching greedoid rooted at vertex v 0 is equivalent to the h ⁎-polynomial of the root polytope of the dual of the graphic matroid.

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We examine the coefficients in front of Chern numbers for complex genera, and pay special attention to the Td 1 2-genus, the Γ-genus as well as the Todd genus. Some related geometric applications to hyper-Kähler and Calabi-Yau manifolds are ...

We examine four identities conjectured by Dean Hickerson which complement five modulo 9 Kanade–Russell identities, and we build up a profile of new identities and new conjectures similar to those found by Ali Uncu and Wadim Zudilin.

In this article, we study 2-designs with λ = 2 admitting a flag-transitive and point-primitive almost simple automorphism group G with socle X a finite simple classical group of Lie type. We prove that such a design belongs to an infinite family ...

In 2012, Andrews and Merca proved a truncated theorem on Euler's pentagonal number theorem. Their work has opened up a new study of truncated series. Recently, Ballantine and Merca posed a conjecture on infinite families of inequalities involving ...

Let OG ( 4 ) denote the family of all graph-group pairs ( Γ , G ) where Γ is finite, 4-valent, connected, and G-oriented (G-half-arc-transitive). A subfamily of OG ( 4 ) has recently been identified as ‘basic’ in the sense that all graphs in this ...

Enumeration of hypermaps (or Grothendieck's dessins d'enfants) is widely studied in many fields. In particular, enumerating hypermaps with a fixed edge-type according to the number of faces and genus is one topic of great interest. The first ...

Let H be an HD0L-system. We show that there are only finitely many primitive words v with the property that v k, for all integers k, is an element of the factorial language of H. In particular, this result applies to the set of all factors of a ...

A group code is a linear code which can be realized as a two-sided ideal of a group algebra over a finite field. When the characteristic of the field is prime to the order of the group, we will give explicit expressions for primitive central ...

We prove several linkage properties of graphs with flows, generalizing some results on linkage of graphs. This translates in properties of connectedness through codimension one of certain posets. For example, the poset of flows and the posets of ...