Discrete Multiplier Sequences: Infinite Support and Low Finite Rank
Year: 2026
Type: preprint
Abstract: A discrete multiplier sequence acts diagonally in the falling-factorial basis and preserves polynomials whose zeros are nonnegative and separated by at least one. We characterize the sequences of infinite support as the nonnegative, nondecreasing classical multiplier sequences after a common sign normalization. This establishes the infinite-support case of a conjecture of Brändén, Krasikov, and Shapiro. A three-term sequence gives a counterexample to the unrestricted statement. We classify sequences of ranks three and four, give sharp rank-three tests for bounded input degree, and describe the interval of admissible values of the last coefficient at finite rank. We also prove sharp Wasserstein bounds for the ordered zero map and characterize the sequences whose entrywise powers preserve the class for arbitrarily small positive exponents. The deposit includes the article, its LaTeX source, and reproducible exact computations.
Source: Figshare
Author: Akihiro Koide
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225771683
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