104
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JCT
2016
10 years 28 days 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...
JCT
2016
10 years 28 days 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...
104
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JCT
2016
10 years 28 days 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...
158
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JCT
2016
10 years 28 days 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 ...
JCT
2016
10 years 28 days 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...
JCT
2016
10 years 28 days 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.
JCT
2016
10 years 28 days 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...
JCT
2016
10 years 28 days 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...
JCT
2016
10 years 28 days ago
2016
JCT
2016
10 years 28 days ago
2016
The essential fact behind the so-called field-descent method is that certain cyclotomic integers necessarily are contained in relatively small fields and thus must have relative...