Related papers: Unique path partitions: Characterization and Congr…
In this paper we introduce a class of sequences connected with the $m$--ary partition function and investigate their congruence properties. In particular, we get facts about the sequences of $m$--ary partitions $(b_{m}(n))_{m\in\mathbb{N}}$…
We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output…
Congruences for stochastic automata are defined, the correspondin factor automata are constructed and investigated for automata ove analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
In this note we show that pattern matching in permutations is polynomial time reducible to pattern matching in set partitions. In particular, pattern matching in set partitions is NP-Complete.
We generalize the idea of cofinite groups, due to B. Hartley. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions. The idea of constructing a cofinite graph starts…
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…
We prove the uniqueness, the functoriality and the naturality of cylinder objects and path objects in closed simplicial model categories.
We define a class of expressions for the multiple zeta function, and show how to determine whether an expression in the class vanishes identically. The class of such identities, which we call partition identities, is shown to coincide with…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Recently the author introduced two new integer partition quadruple functions, which satisfy Ramanujan-type congruences modulo $3$, $5$, $7$, and $13$. Here we reprove the congruences modulo $3$, $5$, and $7$ by defining a rank-type…
This is a survey of results in the enumeration of lattice paths.
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
In graph theory and its practical networking applications, e.g., telecommunications and transportation, the problem of finding paths has particular importance. Selecting paths requires giving scores to the alternative solutions to drive a…
In this paper we give Pfaffian expressions and constant term identities for the enumeration problems presented by Mills, Robbins and Rumsey (``Self-complementary totally symmetric plane partitions'' J. Combin. Theory Ser. A, 42, 277--292),…
In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…
Define a "nuclear partition" to be an integer partition with no part equal to one. In this study we prove a simple formula to compute the partition function $p(n)$ by counting only the nuclear partitions of $n$, a vanishingly small subset…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…