Electronic Journal Of Combinatorial Number Theory

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY x 200x Axx 5 could ﬁt into four rows. M l with n 2k 4m 2l 4 and mk nl 1.

Journal Of Group Theory Ahead Of Print Just Accepted

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 6 2006 A30 2 The following result due to Gao 8 see also 10 Proposition 579 connects these two invariants.

Electronic journal of combinatorial number theory. Using these facts we can. The best unconditional result. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 4 2004 A10 3 RGH cG1H11where cG is the number of vertices of the largest component of Gand H is the chromatic number of H.

An exhaustive calculation ﬁnds that three integers abc satisfy Equations 2 and 3 if and only if they fall into one or more of the following types. The investigation of these invariants has a long tradition and in recent years the investigation of these invariants and of the according inverse problems ie the investigation of the structure of extremal sequences with and in particular without the respective properties. The smallest exponent k such that p.

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 2008 A43 ON THE FROBENIUS PROBLEM FOR GEOMETRIC SEQUENCES Amitabha Tripathi Department of Mathematics Indian Institute of Technology Hauz Khas New Delhi 110016 India atripathmathsiitdacin Received. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 5 2005 A19 4 zeroes of the Riemann zeta function would imply that for any large l there is a prime p 1 mod l such that p. If we set x 0 in 21 and note that xpG 31 1 x is actually a polynomial in x then we see that each term with the exception of c 0 is congruent to 0 mod p.

For a permutation π of the set 012 deﬁne the 3-coloring c π of the nonzero rational numbers by c πq cq for q Q 0 and c πq πc2q for q Q 1. By Theorem 2 in 13 if f0 contains a cycle of length one it contains at most three distinct terms and if it contains a cycle of length two it contains at most four distinct terms. For example all the solutions of the Diophantine equation.

We welcome original research articles in combinatorics and number theory with a preference for those that have a connection to both fields. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 72 2007 A09 3 In Sections 3-6 we show how to use the guidelines of Section 2 strategically to solve some nontrivial enumerationproblemsin the theory of partitionsand compositions. Consider the 3-coloring c of Q 0 given by c 0q i if and only if v 2q 2i mod 6.

If G is a ﬁnite abelian group of order n then EG DGn1. Since a board need not be rectangular a row or column can be formed by only one square. In particular if n 5 G C nand H W 4 or W 5 then we have RC nW 4 2n1 and RC nW 5 3n2 respectively.

41012 Sevilla Spain jmarinuses J. It is published with the help of Colgate University Charles University and DIMATIA. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 2007 A14 ON THE FROBENIUS NUMBER OF FIBONACCI NUMERICAL SEMIGROUPS JM.

Ramırez Alfonsın Combinatoire et Optimisation UniversitePierr e et Marie Curie. N k 0 mod n. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY x 200x Axx 2 There are many papers in the literature treating Diophantine equations involving binomial coeﬃcients.

Any 01-matrix with row sum vector R and column sum vector S can be transformed into any other 01-matrix with row sum vector R and column sum vector S via interchange operations. Abc are drawn from a set of one or two consecutive integers or abc is any per-. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 2007 G07 5 These two conditions can only be met by certain choices of the exponents abc.

Subscriptions to INTEGERS are free. We enumerate the rows of a board from top down and its columns from left to right as is common when labeling the rows and columns of a matrix. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY52 2005 A07 2 In 1961 Erdos Ginzburg and Ziv showed that any sequence of 2m 1 terms from an abelian group of order m contains an m-term zero-sum subsequence 6.

For the particular group ZnZ the following generalization of EG was considered in 2 recently. In 1967 Mann gave an easy extension. Hence c 0 0 mod p.

Let n N and assume A ZnZ. Their result inspired numerous generalizations in extremal combinatorics. N k.

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 6 2006 A24 5 but also G 30 G 31 0 mod p 23 by a well-known congruence which is easy to prove. Binomial Coeﬃcients Divisible By n In this section we characterize all values k 1 k n 1 such that. Various results are known concerning the divisibility of binomial coeﬃcients by a positive integer.

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 2008 A02 2 Theorem 1 Ryser 195714. Integers is a refereed electronic journal devoted to research in the area of combinatorial number theory. It is published with the help of the University of West Georgia Charles University and DIMATIA.

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 2007 A44 3 1. INTEGERS is a refereed electronic journal devoted to research in the area of combinatorial number theory. An exhaustive calculation ﬁnds that three integers abc satisfy Equations 2 and 3 if and only if they fall into one or more of the following types.

Sections 3 and 4 address well-studied problems included as warm-up exercises to illustrate the approach. One of the most useful of these is the so-called Kummers Theorem. This gives rise to the notion of a Ryser class 15.

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 72 2007 A01 4 and only if v 2q is even. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 2007 G07 5 These two conditions can only be met by certain choices of the exponents abc. ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 2007 A21 2 notation we refer to Section 2.

ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 2007 A26 4 Since f0 is ﬁnite 0 must eventually be periodic. Similarly if we set x 1 in 21 then.

100 Best Selling Number Theory Books Of All Time Bookauthority