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Recursively abundant and recursively perfect numbers

TFT. Fink Arxiv

Ample & pristine numbers

Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.

Recursively divisible numbers

TFT. Fink Arxiv

Recursively divisible numbers

Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on.

The mathematical structure of innovation

TFT. FinkITI. Teimouri Arxiv

The mathematical structure of innovation

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

Eigenvalues of subgraphs of the cube

BBJLSL European Journal of Combinatorics

Eigenvalues of subgraphs of the cube

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3 PLOS ONE

Resolution of ranking hierarchies in directed networks

Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications

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4 Nature Communications

Serendipity and strategy

In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

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3 Forum of Mathematics, Sigma

Transference for the Erdős-Ko-Rado theorem

Two constructions for an intersecting family of r-sets.

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5 Physical Review E

Assessing self-assembly

The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.

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3 EPL

Strategy for conkers

In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.