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JCT
1998
68views more  JCT 1998»
13 years 11 months ago
A Note on the Trinomial Analogue of Bailey's Lemma
Recently, Andrews and Berkovich introduced a trinomial version of Bailey’s lemma. In this note we show that each ordinary Bailey pair gives rise to a trinomial Bailey pair. This ...
S. Ole Warnaar
JCT
1998
122views more  JCT 1998»
13 years 11 months ago
Counting 1-Factors in Regular Bipartite Graphs
We show that any k-regular bipartite graph with 2n vertices has at least ((k−1)k−1 kk−2 )n perfect matchings (1-factors). Equivalently, this is a lower bound on the permanent...
Alexander Schrijver
JCT
1998
70views more  JCT 1998»
13 years 11 months ago
Partitions into Distinct Parts and Elliptic Curves
Let Q(N) denote the number of partitions of N into distinct parts. If ω(k) := 3k2 +k 2 , then it is well known that Q(N) + ∞X k=1 (−1)k “ Q(N − 2ω(k)) + Q(N − 2ω(−k)...
Ken Ono
JCT
1998
48views more  JCT 1998»
13 years 11 months ago
Triangle-Free Circuit Decompositions and Petersen Minor
Katherine Heinrich, Jiping Liu, Cun-Quan Zhang
JCT
1998
57views more  JCT 1998»
13 years 11 months ago
The Veronese Surface in PG(5, 3) and Witt's 5-(12, 6, 1) Design
A conic of the Veronese surface in PG(5, 3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model K for Witt’s 5–(12, ...
Hans Havlicek
JCT
1998
68views more  JCT 1998»
13 years 11 months ago
Rook Theory and t-Cores
If t is a positive integer, then a partition of a non-negative integer n is a t−core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These...
James Haglund, Ken Ono, Lawrence Sze
JCT
1998
100views more  JCT 1998»
13 years 11 months ago
2-Partition-Transitive Tournaments
Given a tournament score sequence s1 ≥ s2 ≥ · · · ≥ sn, we prove that there exists a tournament T on vertex set {1, 2, . . . , n} such that the degree of any vertex i is ...
Barry Guiduli, András Gyárfás...
JCT
1998
99views more  JCT 1998»
13 years 11 months ago
From Hall's Matching Theorem to Optimal Routing on Hypercubes
We introduce a concept of so-called disjoint ordering for any collection of finite sets. It can be viewed as a generalization of a system of distinctive representatives for the s...
Shuhong Gao, Beth Novick, Ke Qiu
JCT
1998
44views more  JCT 1998»
13 years 11 months ago
A Note on Difference Sets
Hikoe Enomoto, Mariko Hagita, Makoto Matsumoto
JCT
1998
55views more  JCT 1998»
13 years 11 months ago
New Results for the Martin Polynomial
Joanna A. Ellis-Monaghan