COMBINATORICS
2000
14 years 8 days ago
2000
We prove a conjecture of Cohn and Propp, which refines a conjecture of Bosley and Fidkowski about the symmetry of the set of alternating sign matrices (ASMs). We examine data aris...
COMBINATORICS
2000
14 years 8 days ago
2000
Bound polysemy is the property of any pair (G1, G2) of graphs on a shared vertex set V for which there exists a partial order on V such that any pair of vertices has an upper boun...
COMBINATORICS
2000
14 years 8 days ago
2000
Let d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1), (1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n) with permitted steps from th...
COMBINATORICS
2000
14 years 8 days ago
2000
We constructively prove that the partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain. In other words, there exists an infini...
COMBINATORICS
2000
14 years 8 days ago
2000
In a previous paper it was established that there are at least 27 non-isomorphic strongly regular (40, 12, 2, 4) graphs. Using a different and more efficient method we have re-inv...
COMBINATORICS
2000
14 years 8 days ago
2000
We define type-B analogues of combinatorial statistics previously studied on noncrossing partitions and show that analogous equidistribution and symmetry properties hold in the ca...
COMBINATORICS
2000
14 years 8 days ago
2000
A counterexample is presented to Gy. Elekes's conjecture concerning the existence of long 2-colored paths in properly colored graphs. A modified version of the conjecture is ...
COMBINATORICS
2000
14 years 8 days ago
2000
The lattice of the set partitions of [n] ordered by refinement is studied. Suppose r partitions p1, . . . , pr are chosen independently and uniformly at random. The probability tha...
COMBINATORICS
2000
14 years 8 days ago
2000
Short, bijective proofs of identities for multisets of `hook pairs' (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally foun...
COMBINATORICS
2000
14 years 8 days ago
2000
We study the limiting distribution of the height in a generalized trie in which external nodes are capable to store up to b items (the so called b-tries). We assume that such a tr...