102
Voted
JCT
2016
9 years 11 months ago
2016
Given a finite point set P ⊂ Rd , a k-ary semi-algebraic relation E on P is the set of k-tuples of points in P, which is determined by a finite number of polynomial equations ...
104
Voted
JCT
2016
9 years 11 months ago
2016
There are numerous combinatorial objects associated to a Grassmannian permutation wλ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook...
97
Voted
JCT
2016
9 years 11 months ago
2016
A classic theorem in combinatorial design theory is Fisher’s inequality, which states that a family F of subsets of [n] with all pairwise intersections of size λ can have at mo...
88
Voted
JCT
2016
9 years 11 months ago
2016
We introduce a notion of bipartite minors and prove a bipartite analog of Wagner’s theorem: a bipartite graph is planar if and only if it does not contain K3,3 as a bipartite min...
97
Voted
JCT
2016
9 years 11 months ago
2016
The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for s...
151
Voted
JCT
2016
9 years 11 months ago
2016
Abstract. We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we ...
88
Voted
JCT
2016
9 years 11 months ago
2016
We define and study a recurrence relation in Z3 , called the hexahedron recurrence, which is similar to the octahedron recurrence (Hirota bilinear difference equation) and cube re...
82
Voted
JCT
2016
9 years 11 months ago
2016
It is proved that, for a prime number p, showing that an n-element matroid is not representable over GF(p) requires only O(n2 ) rank evaluations.
75
Voted
JCT
2016
9 years 11 months ago
2016
Let a planar algebraic curve C be defined over a valuation field by an equation F(x, y) = 0. Valuations of the coefficients of F define a subdivision of the Newton polygon ∆ o...
84
Voted
JCT
2016
9 years 11 months ago
2016
A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly increases the diameter. In this paper, we prove several results related to a conje...