Weighted Davenport constant

Weighted zero-sum free sequences to Weighted zero-sum subsequences are monotone in the weight set

• Weighted zero-sum free sequences
• Weighted Davenport constant
• The weighted Davenport constant as a least length
• Prefixes of weighted zero-sum free sequences
• Upper bound for the weighted Davenport constant
• Lower bound for the weighted Davenport constant
• When the weighted Davenport constant is infinite
• Weighted Davenport constant of the trivial group
• Davenport constant of the group of order two
• Units modulo n
• Squares of units modulo n
• Nonzero squares modulo \(n\)
• Weighted zero-sum sequences
• Weighted zero-sum subsequences
• Consecutive weighted zero-sum subsequences
• Representatives of a set of residues
• Membership in the weight representatives
• Lengths forcing a consecutive weighted zero sum
• Weighted consecutive zero-sum constant
• Weighted zero-sum subsequences are monotone in the weight set

The one-term zero sequence has a square-weighted zero sum to Square-weighted constants of nonsquares with even \(2\)-adic valuation

• The one-term zero sequence has a square-weighted zero sum
• Decomposition of the nonzero squares modulo a prime power
• Scaled unit squares modulo a prime power
• Number of nonzero squares modulo a prime power
• Square-weighted zero sums lift from a prime-power component
• Prime-power bound for the square-weighted consecutive constant
• Square-weighted zero sums lift from \(p\) to odd powers \(p^r\)
• Square-weighted zero-sum free unit triples modulo even powers of two
• Three-term sequences without square-weighted zero-sum subsequences
• Square-weighted Davenport constant of even squares is at least four
• Lifting weighted zero sums from p² to an even power of p
• Square-weighted constants modulo \(p^r\), for \(p \ge 2\) and nonzero even \(r\), are at most unit-square constants modulo \(p^2\)
• Consecutive square-weighted constant of an even power of two is at most four
• Square-weighted constants of even squares
• Two units without square-weighted zero sums modulo any prime divisor
• Square-weighted zero-sum free unit pairs lift to odd prime powers
• The square-weighted Davenport constant of an odd modulus is at least three
• Square-weighted Davenport constant for an even 2-adic valuation of at least two
• Consecutive square-weighted constant of an odd prime to an odd power is at most three
• Square-weighted constants of nonsquares with even \(2\)-adic valuation

Consecutive square-weighted constant of an odd power of two is at most two to A nested ceiling identity for divisors

• Consecutive square-weighted constant of an odd power of two is at most two
• Square-weighted constants of numbers with odd \(2\)-adic valuation
• Four-term sequences without square-weighted zero-sum subsequences
• The square-weighted Davenport constant of an odd square is at least five
• Three unit-square cosets sum to every residue modulo an odd prime power
• The square-weighted Davenport constant of an even power of an odd prime is at most five
• The square-weighted Davenport constant of an odd square is five
• Unit-square-weighted consecutive constant modulo 25 equals nine
• Consecutive square-weighted constant of an odd square is at most nine
• Square-weighted consecutive constant of \(p^r\) for prime \(p \ge 7\) and even \(r \ge 4\) is at most five
• Square-weighted consecutive constant five for odd squares with a large prime fourth power
• Four unit terms force a unit-square-weighted zero sum modulo a power of 5
• Square-weighted consecutive constant of \(5^r\) for even \(r \ge 4\) is at most seven
• Square-weighted consecutive constant of squares divisible by 625 is at most seven
• Consecutive square-weighted constant of the square of an odd squarefree number
• Xia's theorem on arithmetic progressions of weights
• Weighted Davenport constant of \(\mathbb{Z}/n\mathbb{Z}\) for the weights prime to \(p\)
• Olson's theorem for groups of rank at most two
• Olson's theorem for abelian \(p\)-groups
• A nested ceiling identity for divisors

Weight sets with weighted Davenport constant \(m\) on \(\mathbb{Z}/n\mathbb{Z}\) to Three-term sums of square-weighted units cover \(\mathbb{Z}_{p^r}\)

• Weight sets with weighted Davenport constant \(m\) on \(\mathbb{Z}/n\mathbb{Z}\)
• Weighted Davenport constant of \(\mathbb{Z}/n\mathbb{Z}\) for the weights \(\{1, \dots, r\}\)
• Initial-interval weights with weighted Davenport constant \(m\)
• Long weighted zero-sum free sequences in groups of rank two
• Weight sets with prescribed weighted Davenport constant on \(\mathbb{Z}/n\mathbb{Z} \times \mathbb{Z}/kn\mathbb{Z}\), divisible case
• Weight sets with prescribed weighted Davenport constant on \(\mathbb{Z}/n\mathbb{Z} \times \mathbb{Z}/kn\mathbb{Z}\), non-divisible case
• Weight sets with weighted Davenport constant \(2m - 1\) on \(\mathbb{Z}/n\mathbb{Z} \times \mathbb{Z}/n\mathbb{Z}\)
• Long weighted zero-sum free sequences in abelian \(p\)-groups
• Weighted Davenport constant of abelian \(p\)-groups, divisible case
• Weighted Davenport constant of abelian \(p\)-groups, non-divisible case
• Weighted Davenport constant of \((\mathbb{Z}/p^e\mathbb{Z})^r\)
• Unit-weighted zero-sum constants of \(\mathbb{Z}_n\)
• Quadratic-residue-weighted zero-sum constants modulo a prime
• Product lower bound for the consecutive weighted zero-sum constant
• Lower bound for the weighted Davenport constant of a product modulus
• The index of the Jacobi symbol kernel
• Units lift to the kernel of the Jacobi symbol across a non-square coprime factor
• Lifting weighted zero sums along a coprime factor
• Unit-weighted zero sums modulo an odd prime power
• Three-term sums of square-weighted units cover \(\mathbb{Z}_{p^r}\)

Three-term sums with prescribed square classes cover \(\mathbb{Z}_{p^r}\) to Consecutive zero-sum constant of a finite abelian group

• Three-term sums with prescribed square classes cover \(\mathbb{Z}_{p^r}\)
• Three unit terms force a square-weighted zero sum modulo \(p^r\)
• Few unit terms force a Jacobi-weighted zero sum
• Three terms coprime to one prime force a Jacobi-weighted zero sum
• Davenport constant for the weights of Jacobi symbol one
• Consecutive constant for the weights of Jacobi symbol one
• Units with equal Jacobi and Legendre symbols form a subgroup of index two
• Lifting the Jacobi kernel into the Jacobi agreement set
• Units modulo a prime divisor lift to units where the Jacobi and Legendre symbols agree
• Chinese remainder lifts into the Jacobi agreement set
• Weighted zero-sum criterion for the Jacobi–Legendre weights
• Davenport constant of the Jacobi–Legendre weights
• Davenport constant of the Jacobi–Legendre weights modulo a product of two primes
• Consecutive constant of the Jacobi–Legendre weights
• Consecutive constant of the Jacobi–Legendre weights modulo a product of two primes
• Weighted Davenport constant of a product with product weights
• Weighted Davenport constant of a product of modules
• Consecutive weighted zero-sum constant of a product with product weights
• Consecutive weighted zero-sum constant of a product of modules
• Consecutive zero-sum constant of a finite abelian group

A block of consecutive coordinates orthogonal to \(a\) vectors of \(\mathbb{Z}_2^m\) to Consecutive weighted zero-sum constant for odd weights

• A block of consecutive coordinates orthogonal to \(a\) vectors of \(\mathbb{Z}_2^m\)
• A block of consecutive integers meeting \(a\) given sets evenly
• Griffiths' criterion for unit-weighted zero sums modulo a prime power
• Davenport constant of \(\mathbb{Z}_2^a\)
• A nonzero vector of \(\mathbb{Z}_2^m\) orthogonal to \(a\) vectors when \(a < m\)
• A nonempty subset of \(\{1, \dots, m\}\) meeting \(a\) given sets evenly
• Zero-sum subsequences of length \(m\) in \(\mathbb{Z}_2^a\)
• A weight-\(m\) vector orthogonal to given vectors of \(\mathbb{Z}_2^{m+a}\)
• An \(m\)-subset of \(\{1, \dots, m + a\}\) meeting \(a\) given sets evenly
• Unit-weighted zero sums of even length in \(\mathbb{Z}_n\)
• Every \(m\)-dimensional subspace of \(\mathbb{Z}_2^{m+a}\) has a vector of weight \(m\)
• Largest subspaces of \(\mathbb{Z}_2^{m+a}\) with no vector of weight \(m\)
• Unit-weighted Erdős–Ginzburg–Ziv constant of \(\mathbb{Z}_n\) for even \(n\)
• Sequences equivalent to the extremal profile have no unit-weighted zero sum of length \(2^r\)
• Structure of extremal sequences for unit-weighted zero sums of length \(2^r\)
• Luca's lemma on unit-weighted zero sums modulo \(2^r\)
• Unit-weighted zero sums of multiples of a prime
• Halving consecutive unit-weighted zero-sum free sequences modulo a power of two
• Consecutive weighted zero-sum constant for interval weights
• Consecutive weighted zero-sum constant for odd weights

Davenport constant of \(\mathbb{Z}_p\) with \(k\)-th power unit weights is at most \(k\) to Weighted zero-sum free pairs for \(k\)-th power weights modulo a prime

• Davenport constant of \(\mathbb{Z}_p\) with \(k\)-th power unit weights is at most \(k\)
• Weighted zero-sum free pairs in a field
• Weighted zero-sum free pairs for a proper subgroup of \(F^\times\)
• Weighted zero-sum free pairs for \(k\)-th power weights modulo a prime

The dependency explorer needs JavaScript and its graph data.

Download the complete graph data.