<p>We prove the consistency of the relation <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10474_2025_1503_Article_IEq1.gif" Format="GIF" Height="64" Rendition="HTML" Resolution="72" Type="Linedraw" Width="109" /> </InlineMediaObject> <EquationSource Format="TEX">$\left(\begin{matrix}\nu \\ \mu \\ \lambda \end{matrix}\right) \rightarrow \left(\begin{matrix} \nu \\ \mu \\ \lambda \end{matrix}\right)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <mtable> <mtr> <mtd> <mi>ν</mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mi>μ</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mi>λ</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mfenced> <mo stretchy="false">→</mo> <mfenced close=")" open="("> <mrow> <mtable> <mtr> <mtd> <mi>ν</mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mi>μ</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow /> <mi>λ</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mfenced> </mrow> </math></EquationSource> </InlineEquation> when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10474_2025_1503_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="228" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda < \mu = \text{cf}(\mu) < \nu = \text{cf} (\nu) \leq 2^{\mu}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo><</mo> <mi>μ</mi> <mo>=</mo> <mtext>cf</mtext> <mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> <mo><</mo> <mi>ν</mi> <mo>=</mo> <mtext>cf</mtext> <mrow> <mo stretchy="false">(</mo> <mi>ν</mi> <mo stretchy="false">)</mo> </mrow> <mo>≤</mo> <msup> <mn>2</mn> <mi>μ</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>.</p>

Hungarian cubes

期刊论文
发表日期：

2025年2月8日

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S. Garti

摘要

We prove the consistency of the relation $\left(\begin{matrix}\nu \\ \mu \\ \lambda \end{matrix}\right) \rightarrow \left(\begin{matrix} \nu \\ \mu \\ \lambda \end{matrix}\right)$ $(\begin{matrix} ν \\ μ \\ λ \end{matrix}) \to (\begin{matrix} ν \\ μ \\ λ \end{matrix})$ when $\lambda < \mu = \text{cf}(\mu) < \nu = \text{cf} (\nu) \leq 2^{\mu}$ $λ < μ = cf (μ) < ν = cf (ν) \leq 2^{μ}$ .