Harry J. Altman

collaborators

4 papers

math.CO2026

A Ring structure on the Class of Combinatorial Games

Harry Altman, Paolo Lipparini

J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games…

math.LO2026

Bounding finite-image sequences of length $I ¨ ^{k}$

Harry Altman

Given a well-quasi-order $X$ and an ordinal $I^\pm$ , the set $s_{I^}^{F} \pm (X)$ of transfinite sequences on $X$ with length less than $I^\pm$ and with finite image is also a well-quasi-order, a…

math.NT2025

Integer complexity: Stability and self-similarity

Harry Altman, Juan Arias de Reyna

Define $∣∣ n ∣∣$ to be the complexity of $n$ , the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. The set $D$ of…

math.LO2025

Maximum linearizations of lower sets in $N^{m}$ with application to monomial ideals

Harry Altman, Andreas Weiermann

We compute the type (maximum linearization) of the well partial order of bounded lower sets in $N^{m}$ , ordered under inclusion, and find it is $I ¨ ^{I ¨ ^{m - 1}}$ . Moreover we…

A Ring structure on the Class of Combinatorial Games

Bounding finite-image sequences of length I¨k

Integer complexity: Stability and self-similarity

Maximum linearizations of lower sets in Nm with application to monomial ideals

Bounding finite-image sequences of length $I ¨ ^{k}$

Maximum linearizations of lower sets in $N^{m}$ with application to monomial ideals