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Alper Ferudun

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#edge computing Open access Oct 2026

On a Question of Benjamini on First-Passage Percolation in Hierarchical Graphs: The Recursive Constant Exceeds the Branching Random Walk Constant

In Question 9.1 of his survey "Euclidean vs. Graph Metric" (2013), Benjamini considers first-passage percolation on the hierarchical graphs G_n obtained by replacing, recursively, every edge by one edge followed by two parallel edges. With independent positive edge weights of law ξ, the source–sink distance satisfies D...

Alper Ferudun · 0 citations
#explainable ai Open access Oct 2026

Higher A-Homotopy Vanishing for Coxeter Chamber Graphs

We prove that the standard Cayley graph of every finite-rank Coxeter system has trivial A-homotopy groups in all degrees at least two. The argument replaces the Coxeter group by the right-angled Coxeter group that retains exactly its commuting relations. All short closed walks lift to the resulting cover, while every f...

Alper Ferudun · 0 citations
#explainable ai Open access Oct 2026

On a Problem of Ferrand and Stoimenow Answered in Print by Rutherford and Ito: A Sharper Signature Bound for the HOMFLY Polynomial of Alternating Links, and a Short Proof that Quasipositive Alternating Links Are Positive

Problem 1.16 of Ohtsuki's list (E. Ferrand, A. Stoimenow) asks whether every alternating link L satisfies σ(L) ≥ min deg_l P_L ≥ min deg_a F_L(a^-1, z), where σ is the signature, P_L(l, m) the HOMFLY polynomial and F_L(a, z) the Kauffman polynomial. Both inequalities are in print: the second is a corollary of Rutherfor...

Alper Ferudun · 0 citations
#edge computing Open access Oct 2026

On Seven Conjectures of Fuchs on Billiard Trajectories in Regular Polygons and Geodesics on the Regular Dodecahedron

In a problem contribution (Arnold Math. J. 7 (2021)), D. Fuchs stated seven conjectures on the billiard trajectories in a regular n-gon which join two vertices (short trajectories) and on their n − 2 types A_0, ..., A_{n−3}, on closed trajectories, and on geodesics on the regular dodecahedron. We decide all seven. The...

Alper Ferudun · 0 citations
#edge computing Open access Sep 2026

Finite Bipartite Graphs as Induced Subgraphs of Subfactor Principal Graphs

Every finite bipartite simple graph occurs as a vertex-induced unrooted subgraph of the principal graph of an irreducible finite-depth inclusion of hyperfinite type II1 factors. For part sizes m and n, an explicit neighborhood-multiplicity parameter q gives index q3^n, with q at most m+1, and depth at most four. The se...

Alper Ferudun · 0 citations
#edge computing Open access Sep 2026

Finite Bipartite Graphs as Induced Subgraphs of Subfactor Principal Graphs

Every finite bipartite simple graph occurs as a vertex-induced unrooted subgraph of the principal graph of an irreducible finite-depth inclusion of hyperfinite type II1 factors. For part sizes m and n, an explicit neighborhood-multiplicity parameter q gives index q3^n, with q at most m+1, and depth at most four. The se...

Alper Ferudun · 0 citations

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