We study the sequence $a(0)=0$, $a(1)=1$ and $a(n)=n-a(n-a(n-a(n-1)))$ for $n\ge 2$, listed as A076502 in the On-Line Encyclopedia of Integer Sequences. We identify $a(n)$ as a two-position shift in the greedy Padovan numeration system, with a finite-state correction. The proof constructs an addition automaton from an...
A sub-quorum coloring is a partial vertex coloring in which every colored vertex sees at least half of its colored closed neighborhood in its own color. Hedetniemi, Hedetniemi, Laskar and Mulder introduced its maximum number of colors, $\psq(G)$, as an open direction in their foundational work on quorum colorings. We e...
A single-file solver organized as a cheapest-first cascade is presented, which combines coefficient tests over structured algebra families, bounded finite-model search, an explicit central-groupoid witness, and several infinite-carrier witnesses and makes no completeness or comparative-superiority claim.
Hao Ma, Wen-Lin Zhang, Manuel Israel Cazares· 0 citations
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