We present new examples of discrete mathematical statements that can be proved from large cardinal hypotheses but not within the usual ZFC axioms for mathematics (assuming ZFC is consistent). These new statements are provably equivalent to Π1 sentences (purely universal statements, logically analogous to Fermat's Last Theorem) in particular provably equivalent to the consistency of strong set t...

The paper describes a few ways in which the concept of a Coxeter group (in its most ubiquitous manifestation, the symmetric group) emerges in the theory of ordinary matroids: • Gale’s maximality principle which leads to the Bruhat order on the symmetric group; • Jordan–Hölder permutation which measures distance between two maximal chains in a semimodular lattice and which happens to be closely ...

We give a Coulson integral formula and Coulson-Jacobs for the p-Schatten energy of bipartite graphs. use these formulas to compare different trees by using quasiorder, establishing maximality paths minimality stars among all trees.

This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Lévy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem (Gapeev in J. Appl. Probab. 44:713–731, 2007; Guo and Shepp in J. Appl. Probab. 38:647–658, 2001; Pedersen in J. Appl. Probab. 37:972–983, 2000), which has its origins in math...

We develop an untyped framework for the multiverse of set theory. $\mathsf{ZF}$ is extended with semantically motivated axioms utilizing new symbols $\mathsf{Uni}(\mathcal{U})$ and $\mathsf{Mod}(\mathcal{U, \sigma})$, expressing that $\mathcal{U}$ a universe $\sigma$ true in $\mathcal{U}$, respectively. Here ranges over augmented language, leading to liar-style phenomena are analysed. The both ...

Geometrical objects with integral side lengths have fascinated mathematicians through the ages. We call a setP = {p1, . . . , pn} ⊂ Z2 a maximal integral point set over Z2 if all pairwise distances are integral and every additional point pn+1 destroys this property. Here we consider such sets for a given cardinality and with minimum possible diameter. We determine some exact values via exhausti...