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Combinatorial Telescoping for an Identity of Andrews on Parity in Partitions
creative telescoping combinatorial telescoping partition q-little Jacobi polynomial
2014/6/3
Recently Andrews proposed a problem of finding a combinatorial proof of an identity on the q-little Jacobi polynomials. We give a classification of certain triples of partitions and find bijections ba...
Cyclic and Quasi-Cyclic LDPC Codes on Row and Column Constrained Parity-Check Matrices and Their Trapping Sets
Quasi-Cyclic LDPC Codes on Row Column Constrained Parity-Check Matrices Their Trapping Sets
2011/2/21
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code gi...
A Functorial Map from Knots in Thickened Surfaces to Classical Knots and Generalisations of Parity
Functorial Map Thickened Surfaces Classical Knots
2010/11/24
We construct a functorial map from knots in thickened surfaces to classical knots. This method uses a natural generalisation of the notion of parity: we localise the information about non-triviality ...
Parity conjectures for elliptic curves over global fields of positive characteristic
Parity conjectures elliptic curves positive characteristic
2010/11/19
We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p > 3$. We also present partial results on the $\ell$-parity conjecture for primes $\ell \neq p$.
Parity balance of the $i$-th dimension edges in Hamiltonian cycles of the hypercube
Hypercube Hamiltonian cycles i-th dimension edges equi-independence number
2010/12/8
Let n 2 be an integer, and let i 2 f0; : : : ; n 1g. An i-th dimension edge in the n-dimensional hypercube Qn is an edge v1v2 such that v1; v2 di er just at their i-th entries. The parity...
Notes on the Parity Conjecture
Notes Parity Conjecture
2010/12/14
The main purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate-Shafarevich group implies the parity conjecture for elliptic curves over number fields. Alo...
On the parity complexity measures of Boolean functions
Computational complexity Communication complexity Parity decision tree Log-Rank conjecture
2012/11/30
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Bool...
Finite element investigations for the construction of composite solutions of even-parity transport equation
Finite element method Boltzmann transport equation variational prin-ciples discontinuous formulation
2009/1/7
Finite element investigations for the construction of
composite solutions of even-parity transport equation
Anwar M. Mirza and Shaukat Iqbal
Abstract. Finite element investigations have been carrie...
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
plane tree Dyck path 2-Motzkin path Catalan number involution
2014/6/3
The problem of counting plane trees with n edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity wa...
Parity considerations in the expansion of Fermat-Pell polynomials
Parity considerations expansion Fermat-Pell polynomials
2010/11/1
For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive ...