
Online Journal of Analytic Combinatorics
ISSN 1931-3365 (online)
The Online Journal of Analytic Combinatorics (OJAC) is a peer-reviewed electronic journal previously hosted by the University of Rochester and now published by Combinatorial Press. OJAC features research articles that span a broad spectrum of topics, including analysis, number theory, and combinatorics, with a focus on the convergence and interplay between these disciplines. The journal particularly welcomes submissions that incorporate one or more of the following elements: combinatorial results derived using analytic methods, analytic results achieved through combinatorial approaches, or a synthesis of combinatorics and analysis in either the methodologies or their applications
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- Research article
- https://doi.org/10.61091/ojac-603
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 6, 2011
- Pages: 1-17 (Paper #3)
- Published: 31/12/2011
Let
- Research article
- https://doi.org/10.61091/ojac-602
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 6, 2011
- Pages: 1-19 (Paper #2)
- Published: 31/12/2011
A word is centrosymmetric if it is invariant under the reverse-complement map. In this paper, we give enumerative results on k-ary centrosymmetric words of length n avoiding a pattern of length 3 with no repeated letters.
- Research article
- https://doi.org/10.61091/ojac-601
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 6, 2011
- Pages: 1-24 (Paper #1)
- Published: 31/12/2011
We consider a bivariate rational generating function
under the assumption that the complex algebraic curve
- Research article
- https://doi.org/10.61091/ojac-508
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-94 (Paper #8)
- Published: 31/01/2010
This paper presents a new construction of the
- Research article
- https://doi.org/10.61091/ojac-507
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-15 (Paper #7)
- Published: 31/01/2010
Let
- Research article
- https://doi.org/10.61091/ojac-506
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-19 (Paper #6)
- Published: 31/01/2010
We prove that a sumset of a TE subset of N (these sets can be viewed as “aperiodic” sets) with a set of positive upper density intersects any polynomial sequence. For WM sets (subclass of TE sets) we prove that the intersection has lower Banach density one. In addition we obtain a generalization of the latter result to the case of several polynomials.
- Research article
- https://doi.org/10.61091/ojac-505
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-24 (Paper #5)
- Published: 31/01/2010
In this paper, we prove the Tiling implies Spectral part of Fuglede’s cojecture for the three interval case. Then we prove the converse Spectral implies Tiling in the case of three equal intervals and also in the case where the intervals have lengths 1/2, 1/4, 1/4. Next, we consider a set Ω ⊂ R, which is a union of n intervals. If Ω is a spectral set, we prove a structure theorem for the spectrum provided the spectrum is assumed to be contained in some lattice. The method of this proof has some implications on the Spectral implies Tiling part of Fuglede’s conjecture for three intervals. In the final step in the proof, we need a symbolic computation using Mathematica. Finally with one additional assumption we can conclude that the Spectral implies Tiling holds in this case.
- Research article
- https://doi.org/10.61091/ojac-504
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-4 (Paper #4)
- Published: 31/01/2010
We show that if
- Research article
- https://doi.org/10.61091/ojac-503
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-4 (Paper #3)
- Published: 31/01/2010
We provide further explanation of the significance of an example in a recent paper of Wolf in the context of the problem of finding large subspaces in sumsets.
- Research article
- https://doi.org/10.61091/ojac-502
- Full Text
- Online Journal of Analytic Combinatorics
- Issue 5, 2010
- Pages: 1-24 (Paper #2)
- Published: 31/01/2010
Lucy Slater used Bailey’s
In the present paper, we apply the same techniques to Chu’s
In re-examining Slater’s work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters. Further, we also find new general Bailey pairs (containing one or more free parameters) which are also implied by the
Slater used the Jacobi triple product identity (sometimes coupled with the quintuple product identity) to derive her infinite products. Here we also use other summation formulae (including special cases of the