A note on solid partitions
A note on some Mahonian statistics.
A note on some polynomial identities
A note on symmetric powers of the standard representation of .
A note on the determinant of a Toeplitz-Hessenberg matrix
The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.
A note on the distribution of the three types of nodes in uniform binary trees.
A note on the exact expected length of the th part of a random partition.
A note on the modified -Bernstein polynomials.
A note on the number of associative triples in finite commutative Moufang loops
A note on the number of derangements.
A note on the number of squares in a partial word with one hole
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence starts. In this paper, we investigate squares in partial words with one hole, or sequences over a finite alphabet that have a “do not know” symbol or “hole”. A square in a partial word over a given alphabet has the form uv where u is compatible with v, and consequently, such square is...
A note on the -binomial rational root theorem.
A note on the -Genocchi numbers and polynomials.
A note on the Rogers-Fine identity.
A -analogue of a formula of Frobenius.
A partition identity with certain applications
A partition of R in two homogeneous and homeomorphic parts
A partition of the Catalan numbers and enumeration of genealogical trees
A special relational structure, called genealogical tree, is introduced; its social interpretation and geometrical realizations are discussed. The numbers of all abstract genealogical trees with exactly n+1 nodes and k leaves is found by means of enumeration of code words. For each n, the form a partition of the n-th Catalan numer Cₙ, that means .
A partition theorem for α-large sets
A permutation regularity lemma.