Skip to content
DraconiticResearch
Search Sources API
194,226 studies31 sourcesUpdated 3 min ago
PreprintCC BY 4.0arXiv

The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori

  • Yotam Svoray
Open at sourcePDFDOICite

Abstract

We use tools and techniques from p-adic analysis and algebraic number theory to study the algebraicity of the hard square entropy constant and its high dimensional analogues. Specifically, we study arithmetic properties of ad(n), the number of independent sets in the d-dimensional discrete torus, and the associated entropy constants κd=limn→∞ad(n)1/nd. It is not known whether κd is algebraic or transcendental for d>1. Using the fact that the sequence ad(pk) converges p-adically for every prime p and other arithmetic facts, we present a collection of criteria for the algebraicity of κd and bound the number of possible values of prime powers pk for which ad(pk)=κdpkd.

Related

  1. Sharp discrete Hardy constants in low dimensions
    Natanael Alpay
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Three-term asymptotics for discrete Hardy--Rellich constants in high dimension
    Carlos Lizama
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Sharp discrete Hardy constants in dimensions three and four and strict upper bounds from dimension nine
    Carlos Lizama
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Majorization, Entropy and Concentration Inequalities for Discrete α-Concave Random Variables
    Abdulmajeed Alqasem, Heshan Aravinda, Arnaud Marsiglietti
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  5. Bias-Corrected Estimators for Joint Entropy, Conditional Entropy, and Mutual Information in the Discrete Bivariate Case: Theory and an Application to Motor Insurance
    Amadou Diadie Ba
    arXivPreprintCC BY 4.0Full textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{svoray2026algebraicity,
  title = {{The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori}},
  author = {Yotam Svoray},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.28332},
  eprint = {2608.28332},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28332},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori
AU  - Yotam Svoray
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2608.28332
UR  - https://arxiv.org/abs/2608.28332
AB  - We use tools and techniques from p-adic analysis and algebraic number theory to study the algebraicity of the hard square entropy constant and its high dimensional analogues. Specifically, we study arithmetic properties of a_d(n), the number of independent sets in the d-dimensional discrete torus, and the associated entropy constants κ_d=lim_n→∞a_d(n)^1/n^d. It is not known whether κ_d is algebraic or transcendental for d>1. Using the fact that the sequence a_d(p^k) converges p-adically for every prime p and other arithmetic facts, we present a collection of criteria for the algebraicity of κ_d and bound the number of possible values of prime powers p^k for which a_d(p^k)=κ_d^p^kd.
ER  -