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math.AC2026
The asymptotic surjective number and F-surjective signature
Ilya Smirnov, Kevin Tucker
We study two invariants measuring the asymptotic abundance of surjections between modules. We prove that Hashimoto's asymptotic surjective number is attained over local rings, henc…
math.AG2026
Perfectoid Pure and Signature Pairs
Hanlin Cai, Anne Fayolle, Linquan Ma +4
We extend perfectoid purity and related invariants to divisor pairs in mixed characteristic. The resulting purity condition agrees with -purity of pairs in characteristic as…
math.CO2026
Maximal Order Type and Width of the h-Preorder on Finite Labeled Trees
Ilya Smirnov
We establish tight bounds for the width and maximal order type of the h-preorder on Q-labeled trees in terms of the corresponding invariants of well-quasi-order Q.