Author

A. Siemaszko

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Preprint Sep 2026

A note on the diameter of graphs of two-dimensional simplex codes

Let $\Gamma^s(2,q)$ be the graph induced in the Grassmann graph by the $q$-ary simplex codes of dimension 2. For $q=4$, this graph is known to have diameter 3. We prove that the same diameter occurs for every prime power $q\geq5$. Together with the elementary cases $q=2,3$, this gives diam$\Gamma^s(2,q)=0,2,3$ for $q=2...

A. Siemaszko · 0 citations

Preprint Jun 2026

An Efficient Algorithm for Estimating Prime Counts

We develop the Samojluk--Siemaszko (S--S) estimator for the prime-counting function $\pi(x)$ using a non-uniform partition generated by generalized triangular numbers. A cold-start evaluation uses $\big O(\sqrt{x})$ local terms, whereas consecutive partition nodes can be processed with amortized $\big O(1)$ update cost...

Artur Samojluk, A. Siemaszko · 0 citations