On a Conjecture of Peter Borwein

On a Conjecture of Chalk

✍ Ping Ding 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 261 KB

Let f # Z[x] with degree k and let p be a prime. By a complete trigonometric sum we mean a sum of the form S(q, f )= q x=1 e q ( f (x)), where q is a positive integer and e q (:)=exp(2?if (x)Âq). Professor Chalk made a conjecture on the upper bound of S(q, f ) when q is a prime power. We prove Chalk

On a Conjecture of Woodall

✍ Hao Li 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 164 KB

Dirac proved in 1952 that every 2-connected graph of order n and minimum degree k admits a cycle of length at least minfn; 2kg: As a possible improvement, Woodall conjectured in 1975 that if a 2-connected graph of order n has at least n 2 þ k vertices of degree at least k; then it has a cycle of len

On a Conjecture of Foulkes

✍ Suzie C. Dent; Johannes Siemons 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 172 KB

Suppose that ⍀ s 1, 2, . . . , ab for some non-negative integers a and b. Denote Ž . by P a, b the set of unordered partitions of ⍀ into a parts of cardinality b. In this Ž . paper we study the decomposition of the permutation module C P a, b where C is Ž . the field of complex numbers. In particula

On a Conjecture of Ash

✍ Adrian Barbu 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 82 KB

In this paper we prove a particular case of a conjecture of Ash that states the existence of Galois representations associated to Hecke eigenclasses in cohomology.

On a Conjecture of Chowlaet al.

✍ B. Sury 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 147 KB

We prove some congruences for the numbers In particular, we show that the numbers a p = k ( p k ) 2 ( p+k k ) 2 are congruent to 5 modulo p 3 for any prime p 5, thereby proving a conjecture of Chowla et al. (J. Number Theory 12 (1980), 188 190). ## 1998 Academic Press In particular, the conjectur

On Extensions of a Conjecture of Gallai

✍ André E. Kézdy; Hunter S. Snevily 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 307 KB

A graph G is k-critical if it has chromatic number k but every proper subgraph of G has a (k&1)-coloring. We prove the following result. If G is a k-critical graph of order n>k 3, then G contains fewer than n&3kÂ5+2 complete subgraphs of order k&1.