Related papers: An alternative to Vaughan's identity
A variation on the splitting principle
The non-standard identity concept developed in the Homotopy Type theory allows for an alternative analysis of Frege's famous Venus example, which explains how empirical evidences justify judgements about identities and accounts for the…
Using Ramanujan's identities and the Weierstrass-Enneper representation of minimal surfaces and the analogue for Born-Infeld solitons, we derive further non-trivial identities.
We solve the word problem of the identity $x(yz) = (xy)(yz)$ by investigating a certain group describing the geometry of that identity. We also construct a concrete realization of the free system of rank~1 relative to the above identity
We find conditions equivalent to some commutator identities considered in Part I
Classical binomial identities are established by giving probabilistic interpretations to the summands. The examples include Vandermonde identity and some generalizations.
In a Hom-superalgebra, a super-identity equivalent to the Hom-Malcev super-identity is found.
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…
This overview paper defends an augmented cognitively oriented generic-design hypothesis: there are both significant similarities between the design activities implemented in different situations and crucial differences between these and…
We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…
Models of interacting social agents often represent agents as very simple entities having a small number of degrees of freedom, as exemplified by binary opinion models for instance. Understanding how such simple individual characteristics…
Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely…
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
We present a simple alternative viewpoint on Hodge-Newton indecomposability, illustrating its explanatory value through a uniform proof of a combinatorial identity arising from affine Deligne-Lusztig varieties with finite Coxeter part.
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
Instead of dealing with cumbersome binomial identities, we prove Callan's result using generating functions.
Facial expressions are a form of non-verbal communication that humans perform seamlessly for meaningful transfer of information. Most of the literature addresses the facial expression recognition aspect however, with the advent of…
In this paper, we show combinatorial identities that represent powers of positive integers using multinomial coefficients, which do not come from the multinomial theorem and the multinomial Vandermonde's convolution.
In this paper, based on the WZ theory, a very succinct new proof, of an identity by Chaundy and Bullard, was given.
Sury's 2014 proof of an identity for Fibonacci and Lucas numbers (Identity 236 of Benjamin and Quinn's 2003 book: {\em Proofs that count: The art of combinatorial proof}) has excited a lot of comment. We give an alternate, telescoping,…