The enumeration of generalised alternating subsets with congruences

✍ Scribed by I.P. Goulden; D.M. Jackson

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 595 KB
• Volume: 22
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(78)90118-8

✦ Synopsis

We &XV that a number of problems involving the en jmeration of alternating subsets of integers may be solved by a direct method as special cases of the enumeration of configurations which w have termed (2, q)-sequences.

In this paper we consider a class of enumeration problems which have received attention recently. It contains a number of well-known problems including the Terquem Problem, the Slcolem Problem and their various generalisations. Each of these may be obtained by specialising a configuration, kfned in Section 2, called an (I, a)-sequence. Special cases are treated in Section 3. We denote the sum of the elements of ? vector x by S(X). The integer part of a real number y is denoted by [y]. An G;ii$pty sL;m is conventionally zero. A sequence over Z&=(1,. . . JV} is an ele:ncnt of 'JT+,(Z&)i snd h,= H&J(O). The coefficient of x" in the Laurent serzes expansion of f(i) at the origin is denoted by [x"lf(x). Throughout this gaper