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math.CO2024
Links and the Diaconis-Graham Inequality
Christopher Cornwell, Nathan McNew
In 1977 Diaconis and Graham proved two inequalities relating different measures of disarray in permutations, and asked for a characterization of those permutations for which equali…
math.CO2020
Unknotted cycles
Christopher R. Cornwell, Nathan McNew
Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagra…
math.CO2019
Counting pattern-avoiding integer partitions
Jonathan Bloom, Nathan McNew
A partition is said to contain another partition (or pattern) if the Ferrers board for is attainable from under removal of rows and columns. We say avoids i…