Related papers: Calculus proofs of some combinatorial inequalities
Recently, Komatsu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we consider the new concept of higher-order Cauchy numbers and polynomials which generalize…
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus' inequalities. Our results…
In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then apply these classes of functions to present several operator Azc\'{e}l and Minkowski type inequalities…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
We present a proof net calculus for the Displacement calculus and show its correctness. This is the first proof net calculus which models the Displacement calculus directly and not by some sort of translation into another formalism. The…
We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike $\lambda$-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names…
At the first part of the paper we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Ward solution of…
In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
Using a natural representation of a $1/s$-concave function on $\mathbb{R}^d$ as a convex set in $\mathbb{R}^{d+1},$ we derive a simple formula for the integral of its $s$-polar. This leads to convexity properties of the integral of the…
We prove that a general class of measures, which includes $\log$-concave measures, is $\frac{1}{n}$-concave according to the terminology of Borell, with additional assumptions on the measures or on the sets, such as symmetries. This…
We study the computational expressivity of proof systems with fixed point operators, within the 'proofs-as-programs' paradigm. We start with a calculus muLJ (due to Clairambault) that extends intuitionistic logic by least and greatest…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
In this note we demonstrate that a number of case-heavy combinatorial proofs in the mathematical phylogenetics literature can be proven more compactly using computational support. We use these techniques to also prove several new…
We disprove a recent conjecture regarding discrete distributions and their generating polynomials stating that strong log-concavity implies log-submodularity.
In our previous paper [SIMAX 31 n.3 1491-1506(2010)], we studied the condition metric in the space of maximal rank matrices. Here, we show that this condition metric induces a Lipschitz-Riemann structure on that space. After investigating…
Deciding whether a given function is quasiconvex is generally a difficult task. Here, we discuss a number of numerical approaches that can be used in the search for a counterexample to the quasiconvexity of a given function $W$. We will…
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…