Author

Pedro M. M. de Castro

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Preprint Sep 2026

Ehrhart $h^*$-polynomials of $(132,213)$-avoiding permutation polytopes: A repair cone and eventual real-rootedness

Let $P_d(132,213)$ be the convex hull of the permutations in $S_d$ that avoid $132$ and $213$, and let $H_d(t)$ be its Ehrhart $h^*$-polynomial, defined by $\sum_{m\ge0}|mP_d(132,213)\cap\mathbb{Z}^d|t^m=\frac{H_d(t)}{(1-t)^d}$. We give an explicit lattice equivalence between this polytope, a path-Laplacian deficit pol...

P. D. de Castro · 0 citations

Preprint Aug 2026

Optimal exponential memory for sequential Euclidean connections: edge-power costs and phase transitions

We study the edge-power cost of the labelled tree generated by the $\gamma$-strategy, a constant-gain rule for sequential Euclidean connections. Starting with $x_0=p_0$, each input point $p_i$ is attached to $x_{i-1}$, and the state is updated by $x_i=\gamma x_{i-1}+(1-\gamma)p_i$. Retaining $x_i$ subdivides the insert...

P. D. de Castro · 0 citations

Preprint Aug 2026

Sequential Euclidean connections with exponential memory: distributional performance and adversarial robustness

Comparison with the running mean highlights the stationary insertion-length distribution, its time-homogeneous update, stationary coefficient profile, and fixed effective memory, and its time-homogeneous update, stationary coefficient profile, and fixed effective memory.

P. D. de Castro · 1 citation · ⚡1