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JCT
2016
67views more  JCT 2016»
4 years 5 months ago
Cox rings of moduli of quasi-parabolic principal bundles and the K-Pieri rule
We study a toric degeneration of the Cox ring of the moduli of principal SLm(C) bundles on the projective line, with quasi parabolic data given by the the stabilizer of the highest...
Christopher Manon
JCT
2016
38views more  JCT 2016»
4 years 5 months ago
Unavoidable tournaments
A basic result in Ramsey theory states that any tournament contains a “large” transitive subgraph. Since transitive tournaments contain only transitive subgraphs, it is natura...
Asaf Shapira, Raphael Yuster
JCT
2016
58views more  JCT 2016»
4 years 5 months ago
Packing k-partite k-uniform hypergraphs
Let G and H be k-graphs (k-uniform hypergraphs); then a perfect H-packing in G is a collection of vertex-disjoint copies of H in G which together cover every vertex of G. For any ...
Richard Mycroft
JCT
2016
46views more  JCT 2016»
4 years 5 months ago
Semi-algebraic Ramsey numbers
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 ...
Andrew Suk
JCT
2016
98views more  JCT 2016»
4 years 5 months ago
Combinatorics of diagrams of permutations
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...
Joel Brewster Lewis, Alejandro H. Morales
JCT
2016
43views more  JCT 2016»
4 years 5 months ago
Almost-Fisher families
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...
Shagnik Das, Benny Sudakov, Pedro Vieira
JCT
2016
47views more  JCT 2016»
4 years 5 months ago
Bipartite minors
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...
Maria Chudnovsky, Gil Kalai, Eran Nevo, Isabella N...
JCT
2016
53views more  JCT 2016»
4 years 5 months ago
Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions
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...
Christine Bessenrodt, Vasu Tewari, Stephanie van W...
JCT
2016
327views more  JCT 2016»
4 years 5 months ago
Computing the partition function for graph homomorphisms with multiplicities
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 ...
Alexander I. Barvinok, Pablo Soberón
JCT
2016
54views more  JCT 2016»
4 years 5 months ago
Double-dimers, the Ising model and the hexahedron recurrence
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...
Richard W. Kenyon, Robin Pemantle
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