domino forest

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word 2g, Σᵢεᵢ=g, 2≤g≤30

Cyclic binary word

ready

g a

Enter an integer from 1 to g, or leave blank to choose a randomly.

forest

scale 100%

⌁

awaiting word

type sequence

J

isogeny partition

λ

Young diagram

σArt

e = p-exp

a

bounds

σArt

e = p-exp

info

geometric realization is assumed; the upper $\sigma_{\mathrm{Art}}$ endpoint also assumes a principal polarization.

about domino forest

ε → Λ²H¹crys → heights → forest → invariants

input

A balanced binary cyclic word with $g$ zeros and $g$ ones. It records the $p$ -adic Frobenius valuations of a cyclic basis for a supersingular $F$ -crystal. Words are normalized up to cyclic rotation.

forest

The tool forms the exterior square and turns the superlevel sets of its normalized height functions into rooted trees. A vertex $U_j$ records an elementary domino type; an edge $V^m$ records its extension weight.

output

The forest determines the displayed type sequence $J$ , isogeny partition $\lambda$ , Artin invariant $\sigma_{\mathrm{Art}}$ , $p$ -exponent, and $a$ -number. The interval plots compare the example with the bounds used in the paper.

scope

This is the cyclic combinatorial case. Unit coefficients are normalized, and the page does not test geometric realizability or the existence of a principal polarization.

Young diagram

r / c