Related papers: Log canonical inversion of adjunction
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
We introduce the three-Catalan triangle, highlighting the three-Catalan numbers along with their recurrence relation and combinatorial interpretation, which allows us to establish their log-convexity. Additionally, we prove that the rows of…
We make some observation on the logarithmic version of K-stability.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
We generalize the formula for the log canonical threshold(LCT) of plane curves over the complex numbers to arbitrary characteristics. Our proof relies purely on valuation theory, instead of on the theory of $D$-modules.
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
We survey recent developments on the Restriction conjecture.
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…
The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.
We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.
In this short note, we show that a result about words which coincide except in one position given as an exercise in Lothaire's Algebraic Combinatorics on Words is false. Moreover, we derive a modified statement which allows us to fix the…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
These informal notes briefly discuss various aspects of Cantor sets.
Several results about the union-closed sets conjecture are presented.
We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive…