JCT
1998
13 years 5 months ago
1998
If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs ...
JCT
1998
13 years 5 months ago
1998
The aim of this note is to point out some combinatorial applications of a lemma of Scarf, proved first in the context of game theory. The usefulness of the lemma in combinatorics...
JCT
1998
13 years 5 months ago
1998
For k > 2 and r ≥ 2, let G(k, r) denote the smallest positive integer g such that every increasing sequence of g integers {a1, a2, . . . , ag} with gaps aj+1 − aj ∈ {1, ....