Jaan Allikvere

Minimal Trees for the Euler Sombor Index Revisited: A Correction and the First Thirteen Minima

Correction and extension of Theorems 3 and 4 of B. Khanra and S. Das, "Euler Sombor index of trees, unicyclic and chemical graphs", MATCH Commun. Math. Comput. Chem. 94 (2025) 525–548 (doi:10.46793/match.94-2.525K). Parts (c) and (d) of Theorem 3 of that paper are incorrect: the...

Inversion monotonicity and asymptotic enumeration of 1324-avoiding permutations with few inversions

Let A(n,k) count the 1324-avoiding permutations of length n with k inversions, let D(n,k) and I(n,k) count the decomposable and indecomposable ones, and put a(k) = sumj=0k p(j)p(k-j), where p is the partition function. We prove A(n,k) ≤ A(n+1,k) for 0 ≤ k ≤ floor(n2 / [20 log2(n+...

Fourteen lonely runners: manuscript, gate certificates, and audit code

Manuscript and complete verification package for the paper "Fourteen lonely runners": a computer-assisted proof of the Lonely Runner Conjecture for fourteen runners (thirteen moving runners, LRC(13)), within the finite-checking framework of Sungkawichai and Trakulthongchai (arXiv...

Finiteness, Prescribed Gaps, and Extremal Growth in Edge Multiset Dimension: manuscript, verification code, and exact small-order census

Manuscript and complete verification package for the paper "Finiteness, Prescribed Gaps, and Extremal Growth in Edge Multiset Dimension". The paper resolves Problems 22–24 and contributes to Problem 21 of the survey by Farhan, Klavžar, Kuziak and Yero (arXiv:2607.10311). Main res...

Distance Polynomials of Extended Double Covers and Their Iterates, with Corrections to Two Formulas for the Eccentric Distance Sum

Correction and extension of two formulas of H. Hua, S. Zhang and K. Xu, "Further results on the eccentric distance sum", Discrete Appl. Math. 160 (2012) 170–180 (doi:10.1016/j.dam.2011.10.002). Theorem 7 of that paper states ξd(G*) = 6ξd(G) + 12W(G) + 2(n−1)ζ(G) + 2n(n−1) for the...

Distance Polynomials of Extended Double Covers and Their Iterates, with Corrections to Two Formulas for the Eccentric Distance Sum

Correction and extension of two formulas of H. Hua, S. Zhang and K. Xu, "Further results on the eccentric distance sum", Discrete Appl. Math. 160 (2012) 170–180 (doi:10.1016/j.dam.2011.10.002). Theorem 7 of that paper states ξd(G*) = 6ξd(G) + 12W(G) + 2(n−1)ζ(G) + 2n(n−1) for the...