Related papers: Meinardus' theorem on weighted partitions: extensi…
This article introduces probabilistic disjunctive normal forms (PDNFs) as a framework for representing and reasoning about uncertainty in logical systems. Unlike classical DNFs, PDNFs assign real-valued weights to variables, encoding…
We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by -1 as proposed by…
The asymptotic form of the average probability to count $N$ indistinguishable identical particles in a small number $r \ll N$ of binned-together output ports of a $M$-port Haar-random unitary network, proposed recently in \textit{Scientific…
Two proofs of the Koml\'os-Major-Tusn\'ady embedding theorems, one for the uniform empirical process and one for the simple symmetric random walk, are given. More precisely, what are proved are the univariate coupling results needed in the…
Representation theory of finite groups portrays a marvelous crossroad of group theory, algebraic combinatorics, and probability. In particular the Plancherel measure is a probability that arises naturally from representation theory, and in…
We use the $q$-binomial theorem, the $q$-Gauss sum, and the ${}_2\phi_1 \rightarrow {}_2\phi_2$ transformation of Jackson to discover and prove many new weighted partition identities. These identities involve unrestricted partitions,…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
In a recent paper, Dousse introduced a refinement of Siladi\'c's theorem on partitions, where parts occur in two primary and three secondary colors. Her proof used the method of weighted words and $q$-difference equations. The purpose of…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in $\mathcal{L}\subset\mathbb{N}$ ($\gcd(\mathcal{L})=1$) and good analytic properties of the corresponding zeta function, generalizing work…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
We give a proof of the multi-party typicality conjecture for the first nontrivial case when there are only two parties. The conjecture itself is motivated by the study of multi-party state merging protocols on quantum systems. Our approach…
The paper presents a discussion on the asymptotic formula for the number of plane partitions of a large positive integer.
We give asymptotic expansions for the moments of the $M_2$-rank generating function and for the $M_2$-rank generating function at roots of unity. For this we apply the Hardy-Ramanujan circle method extended to mock modular forms. Our…
In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel…
We derive the asymptotic formula for $p_n(N,M)$, the number of partitions of integer $n$ with part size at most $N$ and length at most $M$. We consider both $N$ and $M$ are comparable to $\sqrt{n}$. This is an extension of the classical…
A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…
We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
We present families of combinatorial classes described as trees with nodes that can carry one of two types of "flowers": integer partitions or integer compositions. Two parameters on the flowers of trees will be considered: the number of…