Provides a closed-form piecewise quadratic expression for the Frobenius number of shifted squares, obtained via combinatorial reduction, Lagrange's theorem, and generating functions.
Denham, Short generating functions for some semigroup algebras , Electron
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
fields
math.CO 3verdicts
UNVERDICTED 3representative citing papers
A combinatorial reduction of the Frobenius problem to an optimization task produces explicit formulas for g(A), n(A), and s(A) on special sequences and applies MacMahon's partition analysis to count representations.
Extends the stable property of Frobenius numbers to sequences A(a)=(a, ha+dB) yielding a congruence-class characterization of g(A(a)) mod bk for large a, plus explicit formulas for several B.
citing papers explorer
-
On Frobenius Numbers of Shifted Power Sequences
Provides a closed-form piecewise quadratic expression for the Frobenius number of shifted squares, obtained via combinatorial reduction, Lagrange's theorem, and generating functions.
-
A Combinatorial Approach to Frobenius Numbers of Some Special Sequences (Complete Version)
A combinatorial reduction of the Frobenius problem to an optimization task produces explicit formulas for g(A), n(A), and s(A) on special sequences and applies MacMahon's partition analysis to count representations.
-
The Frobenius Formula for $A=(a,ha+d,ha+b_2d,...,ha+b_kd)$
Extends the stable property of Frobenius numbers to sequences A(a)=(a, ha+dB) yielding a congruence-class characterization of g(A(a)) mod bk for large a, plus explicit formulas for several B.