Multi-Schur functions are symmetric that generalize the supersymmetric Schur functions, flagged and refined dual Grothendieck which have been intensively studied by Lascoux. In this paper, we give a new free-fermionic presentation of them. The multi-Schur indexed partition two ``tuples tuples'' indeterminates. We construct family linear bases fermionic Fock space such data prove they correspond...

For every k > 3, we give a construction of planar point sets with many collinear k-tuples and no collinear (k + 1)-tuples.

Computing with sets of tuples (n-ary relations) is often required in programming. This paper presents a new data structure dedicated to the manipulation of large sets of tuples, dubbed sharing tree. The main idea is to share in memory some sub-tuples of the set. We give algorithms for common set operations, that have theoretical complexities proportional to the sizes of the sharing trees given ...

We present sensitivity analysis for results of query executions in a relational model of data extended by ordinal ranks. The underlying model of data results from the ordinary Codd’s model of data in which we consider ordinal ranks of tuples in data tables expressing degrees to which tuples match queries. In this setting, we show that ranks assigned to tuples are insensitive to small changes, i...

An overpartition of the nonnegative integer n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be overlined. Let k ≥ 1 be an integer. An overpartition k-tuple of a positive integer n is a k-tuple of overpartitions wherein all listed parts sum to n. Let pk(n) be the number of overpartition k-tuples of n. In this paper, we will give a sh...

An n-tuple π (not necessarily monotone) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} in which the degree of vi is the ith entry of π. Graphic n-tuples (d (1) 1 , . . . , d (1) n ) and (d (2) 1 , . . . , d (2) n ) pack if there are edge-disjoint n-vertex graphs G1 and G2 such that dG1(vi) = d (1) i and dG2(vi) = d (2) i for all i. We prove that graphic n-tuples π1 and...